LMFDB - Embedded newform 625.2.h.b.274.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(24,625)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([11]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("625.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.h (of order $50$, degree $20$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{50})$
Twist minimal:	no (minimal twist has level 125)
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			274.8
Character	$\chi$	$=$	625.274
Dual form			625.2.h.b.349.8

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.231876 - 0.903097i) q^{2} +(-0.325489 + 0.0620903i) q^{3} +(0.990795 - 0.544694i) q^{4} +(0.131547 + 0.279551i) q^{6} +(2.39974 - 3.30296i) q^{7} +(-1.99818 - 2.12785i) q^{8} +(-2.68724 + 1.06395i) q^{9} +O(q^{10})$	\(q+(-0.231876 - 0.903097i) q^{2} +(-0.325489 + 0.0620903i) q^{3} +(0.990795 - 0.544694i) q^{4} +(0.131547 + 0.279551i) q^{6} +(2.39974 - 3.30296i) q^{7} +(-1.99818 - 2.12785i) q^{8} +(-2.68724 + 1.06395i) q^{9} +(-5.98107 + 1.53568i) q^{11} +(-0.288672 + 0.238811i) q^{12} +(-0.617961 - 1.56079i) q^{13} +(-3.53934 - 1.40132i) q^{14} +(-0.246660 + 0.388674i) q^{16} +(1.35843 - 2.47098i) q^{17} +(1.58396 + 2.18014i) q^{18} +(0.447990 - 2.34845i) q^{19} +(-0.576007 + 1.22408i) q^{21} +(2.77373 + 5.04540i) q^{22} +(-3.56467 - 0.224270i) q^{23} +(0.782505 + 0.568523i) q^{24} +(-1.26626 + 0.919989i) q^{26} +(1.64793 - 1.04581i) q^{27} +(0.578549 - 4.57968i) q^{28} +(2.50206 + 0.316084i) q^{29} +(8.14699 + 4.47885i) q^{31} +(-5.14404 - 1.67140i) q^{32} +(1.85142 - 0.871213i) q^{33} +(-2.54652 - 0.653835i) q^{34} +(-2.08298 + 2.51789i) q^{36} +(0.404186 + 0.256504i) q^{37} +(-2.22475 + 0.139970i) q^{38} +(0.298050 + 0.469651i) q^{39} +(-0.485173 - 7.71160i) q^{41} +(1.23902 + 0.236356i) q^{42} +(-5.98533 + 1.94475i) q^{43} +(-5.08954 + 4.77940i) q^{44} +(0.624023 + 3.27124i) q^{46} +(3.47567 - 3.70121i) q^{47} +(0.0561522 - 0.141824i) q^{48} +(-2.98768 - 9.19512i) q^{49} +(-0.288730 + 0.888621i) q^{51} +(-1.46243 - 1.20983i) q^{52} +(-5.70747 - 2.68573i) q^{53} +(-1.32658 - 1.24574i) q^{54} +(-11.8233 + 1.49363i) q^{56} +0.792208i q^{57} +(-0.294713 - 2.33290i) q^{58} +(2.17390 + 2.62780i) q^{59} +(0.476848 - 7.57928i) q^{61} +(2.15574 - 8.39606i) q^{62} +(-2.93449 + 11.4291i) q^{63} +(-0.374467 + 5.95198i) q^{64} +(-1.21609 - 1.47000i) q^{66} +(-0.591868 - 4.68512i) q^{67} -3.18816i q^{68} +(1.17418 - 0.148334i) q^{69} +(-4.72298 - 4.43517i) q^{71} +(7.63354 + 3.59207i) q^{72} +(5.24267 + 4.33711i) q^{73} +(0.137927 - 0.424497i) q^{74} +(-0.835318 - 2.57085i) q^{76} +(-9.28074 + 23.4405i) q^{77} +(0.355030 - 0.378068i) q^{78} +(2.35405 + 12.3404i) q^{79} +(5.84915 - 5.49272i) q^{81} +(-6.85183 + 2.22629i) q^{82} +(17.6689 + 3.37053i) q^{83} +(0.0960429 + 1.52656i) q^{84} +(3.14415 + 4.95439i) q^{86} +(-0.834019 + 0.0524720i) q^{87} +(15.2190 + 9.65825i) q^{88} +(-0.523867 + 0.633247i) q^{89} +(-6.63818 - 1.70440i) q^{91} +(-3.65401 + 1.71945i) q^{92} +(-2.92985 - 0.951965i) q^{93} +(-4.14848 - 2.28064i) q^{94} +(1.77810 + 0.224627i) q^{96} +(0.164948 - 1.30570i) q^{97} +(-7.61132 + 4.83029i) q^{98} +(14.4387 - 10.4903i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q + 40 q^{4} - 40 q^{6} + 40 q^{9}+O(q^{10}) $ 440 * q + 40 * q^4 - 40 * q^6 + 40 * q^9	$ 440 q + 40 q^{4} - 40 q^{6} + 40 q^{9} - 30 q^{11} + 20 q^{14} + 20 q^{19} - 10 q^{21} - 30 q^{24} + 30 q^{26} + 20 q^{29} - 20 q^{31} - 10 q^{34} - 420 q^{36} - 10 q^{41} - 30 q^{44} + 40 q^{49} + 50 q^{51} - 120 q^{54} - 210 q^{56} - 10 q^{59} - 90 q^{64} + 110 q^{66} - 80 q^{69} - 170 q^{71} - 70 q^{74} + 70 q^{76} + 110 q^{81} - 230 q^{84} + 80 q^{86} - 110 q^{89} - 210 q^{91} - 120 q^{94} + 270 q^{96} - 90 q^{99}+O(q^{100}) $ 440 * q + 40 * q^4 - 40 * q^6 + 40 * q^9 - 30 * q^11 + 20 * q^14 + 20 * q^19 - 10 * q^21 - 30 * q^24 + 30 * q^26 + 20 * q^29 - 20 * q^31 - 10 * q^34 - 420 * q^36 - 10 * q^41 - 30 * q^44 + 40 * q^49 + 50 * q^51 - 120 * q^54 - 210 * q^56 - 10 * q^59 - 90 * q^64 + 110 * q^66 - 80 * q^69 - 170 * q^71 - 70 * q^74 + 70 * q^76 + 110 * q^81 - 230 * q^84 + 80 * q^86 - 110 * q^89 - 210 * q^91 - 120 * q^94 + 270 * q^96 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{21}{50}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.231876	−	0.903097i	−0.163961	−	0.638586i	−0.996423	−	0.0845042i	$-0.973069\pi$
$2$	−0.231876	−	0.903097i	−0.163961	−	0.638586i	0.832462	−	0.554082i	$-0.186931\pi$
$3$	−0.325489	+	0.0620903i	−0.187921	+	0.0358479i	−0.280483	−	0.959859i	$-0.590495\pi$
$3$	−0.325489	+	0.0620903i	−0.187921	+	0.0358479i	0.0925616	+	0.995707i	$0.470495\pi$
$4$	0.990795	−	0.544694i	0.495398	−	0.272347i
$5$		0			0
$5$		0			0
$6$	0.131547	+	0.279551i	0.0537037	+	0.114126i
$7$	2.39974	−	3.30296i	0.907017	−	1.24840i	−0.0611576	−	0.998128i	$-0.519479\pi$
$7$	2.39974	−	3.30296i	0.907017	−	1.24840i	0.968175	−	0.250274i	$-0.0805208\pi$
$8$	−1.99818	−	2.12785i	−0.706464	−	0.752308i
$9$	−2.68724	+	1.06395i	−0.895747	+	0.354651i
$10$		0			0
$11$	−5.98107	+	1.53568i	−1.80336	+	0.463024i	−0.992503	−	0.122219i	$-0.960999\pi$
$11$	−5.98107	+	1.53568i	−1.80336	+	0.463024i	−0.810858	+	0.585243i	$0.800999\pi$
$12$	−0.288672	+	0.238811i	−0.0833326	+	0.0689387i
$13$	−0.617961	−	1.56079i	−0.171392	−	0.432886i	0.818537	−	0.574454i	$-0.194786\pi$
$13$	−0.617961	−	1.56079i	−0.171392	−	0.432886i	−0.989929	+	0.141568i	$0.954786\pi$
$14$	−3.53934	−	1.40132i	−0.945928	−	0.374519i
$15$		0			0
$16$	−0.246660	+	0.388674i	−0.0616650	+	0.0971685i
$17$	1.35843	−	2.47098i	0.329468	−	0.599300i	−0.658748	−	0.752363i	$-0.728914\pi$
$17$	1.35843	−	2.47098i	0.329468	−	0.599300i	0.988216	+	0.153063i	$0.0489139\pi$
$18$	1.58396	+	2.18014i	0.373343	+	0.513863i
$19$	0.447990	−	2.34845i	0.102776	−	0.538770i	−0.893239	−	0.449582i	$-0.851573\pi$
$19$	0.447990	−	2.34845i	0.102776	−	0.538770i	0.996015	−	0.0891879i	$-0.0284272\pi$
$20$		0			0
$21$	−0.576007	+	1.22408i	−0.125695	+	0.267116i
$22$	2.77373	+	5.04540i	0.591362	+	1.07568i
$23$	−3.56467	−	0.224270i	−0.743285	−	0.0467635i	−0.313368	−	0.949632i	$-0.601457\pi$
$23$	−3.56467	−	0.224270i	−0.743285	−	0.0467635i	−0.429917	+	0.902868i	$0.641457\pi$
$24$	0.782505	+	0.568523i	0.159728	+	0.116049i
$25$		0			0
$26$	−1.26626	+	0.919989i	−0.248333	+	0.180425i
$27$	1.64793	−	1.04581i	0.317144	−	0.201266i
$28$	0.578549	−	4.57968i	0.109335	−	0.865479i
$29$	2.50206	+	0.316084i	0.464621	+	0.0586953i	0.354159	−	0.935185i	$-0.384767\pi$
$29$	2.50206	+	0.316084i	0.464621	+	0.0586953i	0.110462	+	0.993880i	$0.464767\pi$
$30$		0			0
$31$	8.14699	+	4.47885i	1.46324	+	0.804425i	0.996785	−	0.0801191i	$-0.0255301\pi$
$31$	8.14699	+	4.47885i	1.46324	+	0.804425i	0.466457	+	0.884544i	$0.345530\pi$
$32$	−5.14404	−	1.67140i	−0.909346	−	0.295464i
$33$	1.85142	−	0.871213i	0.322291	−	0.151659i
$34$	−2.54652	−	0.653835i	−0.436725	−	0.112132i
$35$		0			0
$36$	−2.08298	+	2.51789i	−0.347163	+	0.419648i
$37$	0.404186	+	0.256504i	0.0664478	+	0.0421690i	0.568636	−	0.822589i	$-0.307471\pi$
$37$	0.404186	+	0.256504i	0.0664478	+	0.0421690i	−0.502188	+	0.864759i	$0.667471\pi$
$38$	−2.22475	+	0.139970i	−0.360903	+	0.0227061i
$39$	0.298050	+	0.469651i	0.0477261	+	0.0752043i
$40$		0			0
$41$	−0.485173	−	7.71160i	−0.0757713	−	1.20435i	−0.833777	−	0.552102i	$-0.813826\pi$
$41$	−0.485173	−	7.71160i	−0.0757713	−	1.20435i	0.758005	−	0.652248i	$-0.226174\pi$
$42$	1.23902	+	0.236356i	0.191186	+	0.0364706i
$43$	−5.98533	+	1.94475i	−0.912754	+	0.296572i	−0.727491	−	0.686117i	$-0.759314\pi$
$43$	−5.98533	+	1.94475i	−0.912754	+	0.296572i	−0.185263	+	0.982689i	$0.559314\pi$
$44$	−5.08954	+	4.77940i	−0.767277	+	0.720521i
$45$		0			0
$46$	0.624023	+	3.27124i	0.0920072	+	0.482319i
$47$	3.47567	−	3.70121i	0.506978	−	0.539877i	−0.423658	−	0.905822i	$-0.639254\pi$
$47$	3.47567	−	3.70121i	0.506978	−	0.539877i	0.930636	+	0.365945i	$0.119254\pi$
$48$	0.0561522	−	0.141824i	0.00810487	−	0.0204706i
$49$	−2.98768	−	9.19512i	−0.426811	−	1.31359i
$50$		0			0
$51$	−0.288730	+	0.888621i	−0.0404303	+	0.124432i
$52$	−1.46243	−	1.20983i	−0.202802	−	0.167773i
$53$	−5.70747	−	2.68573i	−0.783981	−	0.368914i	−0.00824102	−	0.999966i	$-0.502623\pi$
$53$	−5.70747	−	2.68573i	−0.783981	−	0.368914i	−0.775740	+	0.631053i	$0.782623\pi$
$54$	−1.32658	−	1.24574i	−0.180525	−	0.169524i
$55$		0			0
$56$	−11.8233	+	1.49363i	−1.57996	+	0.199595i
$57$			0.792208i			0.104931i
$58$	−0.294713	−	2.33290i	−0.0386978	−	0.306324i
$59$	2.17390	+	2.62780i	0.283018	+	0.342110i	0.892795	−	0.450463i	$-0.148741\pi$
$59$	2.17390	+	2.62780i	0.283018	+	0.342110i	−0.609777	+	0.792573i	$0.708741\pi$
$60$		0			0
$61$	0.476848	−	7.57928i	0.0610542	−	0.970428i	−0.841611	−	0.540084i	$-0.818392\pi$
$61$	0.476848	−	7.57928i	0.0610542	−	0.970428i	0.902665	−	0.430344i	$-0.141608\pi$
$62$	2.15574	−	8.39606i	0.273780	−	1.06630i
$63$	−2.93449	+	11.4291i	−0.369711	+	1.43993i
$64$	−0.374467	+	5.95198i	−0.0468083	+	0.743997i
$65$		0			0
$66$	−1.21609	−	1.47000i	−0.149690	−	0.180944i
$67$	−0.591868	−	4.68512i	−0.0723081	−	0.572378i	−0.986095	−	0.166184i	$-0.946856\pi$
$67$	−0.591868	−	4.68512i	−0.0723081	−	0.572378i	0.913787	−	0.406194i	$-0.133144\pi$
$68$		−	3.18816i		−	0.386621i
$69$	1.17418	−	0.148334i	0.141355	−	0.0178573i
$70$		0			0
$71$	−4.72298	−	4.43517i	−0.560515	−	0.526358i	0.351677	−	0.936121i	$-0.385611\pi$
$71$	−4.72298	−	4.43517i	−0.560515	−	0.526358i	−0.912192	+	0.409763i	$0.865611\pi$
$72$	7.63354	+	3.59207i	0.899621	+	0.423329i
$73$	5.24267	+	4.33711i	0.613608	+	0.507621i	0.891517	−	0.452987i	$-0.149641\pi$
$73$	5.24267	+	4.33711i	0.613608	+	0.507621i	−0.277909	+	0.960607i	$0.589641\pi$
$74$	0.137927	−	0.424497i	0.0160337	−	0.0493467i
$75$		0			0
$76$	−0.835318	−	2.57085i	−0.0958176	−	0.294896i
$77$	−9.28074	+	23.4405i	−1.05764	+	2.67129i
$78$	0.355030	−	0.378068i	0.0401992	−	0.0428078i
$79$	2.35405	+	12.3404i	0.264851	+	1.38840i	0.827390	+	0.561628i	$0.189825\pi$
$79$	2.35405	+	12.3404i	0.264851	+	1.38840i	−0.562539	+	0.826771i	$0.690175\pi$
$80$		0			0
$81$	5.84915	−	5.49272i	0.649906	−	0.610302i
$82$	−6.85183	+	2.22629i	−0.756658	+	0.245853i
$83$	17.6689	+	3.37053i	1.93942	+	0.369963i	0.999600	+	0.0282838i	$0.00900420\pi$
$83$	17.6689	+	3.37053i	1.93942	+	0.369963i	0.939816	+	0.341680i	$0.110996\pi$
$84$	0.0960429	+	1.52656i	0.0104791	+	0.166561i
$85$		0			0
$86$	3.14415	+	4.95439i	0.339043	+	0.534246i
$87$	−0.834019	+	0.0524720i	−0.0894162	+	0.00562559i
$88$	15.2190	+	9.65825i	1.62235	+	1.02957i
$89$	−0.523867	+	0.633247i	−0.0555298	+	0.0671240i	−0.797547	−	0.603257i	$-0.793869\pi$
$89$	−0.523867	+	0.633247i	−0.0555298	+	0.0671240i	0.742017	+	0.670381i	$0.233869\pi$
$90$		0			0
$91$	−6.63818	−	1.70440i	−0.695871	−	0.178669i
$92$	−3.65401	+	1.71945i	−0.380957	+	0.179265i
$93$	−2.92985	−	0.951965i	−0.303811	−	0.0987142i
$94$	−4.14848	−	2.28064i	−0.427883	−	0.235230i
$95$		0			0
$96$	1.77810	+	0.224627i	0.181477	+	0.0229259i
$97$	0.164948	−	1.30570i	0.0167479	−	0.132573i	−0.981524	−	0.191340i	$-0.938717\pi$
$97$	0.164948	−	1.30570i	0.0167479	−	0.132573i	0.998272	+	0.0587665i	$0.0187167\pi$
$98$	−7.61132	+	4.83029i	−0.768859	+	0.487933i
$99$	14.4387	−	10.4903i	1.45114	−	1.05432i
$100$		0			0
$101$	7.06765	+	5.13495i	0.703258	+	0.510947i	0.880992	−	0.473132i	$-0.156877\pi$
$101$	7.06765	+	5.13495i	0.703258	+	0.510947i	−0.177734	+	0.984079i	$0.556877\pi$
$102$	0.869461	+	0.0547018i	0.0860894	+	0.00541629i
$103$	−5.39429	−	9.81218i	−0.531516	−	0.966823i	−0.996666	−	0.0815915i	$-0.974000\pi$
$103$	−5.39429	−	9.81218i	−0.531516	−	0.966823i	0.465150	−	0.885232i	$-0.346000\pi$
$104$	−2.08633	+	4.43368i	−0.204581	+	0.434758i
$105$		0			0
$106$	−1.10205	+	5.77716i	−0.107041	+	0.561127i
$107$	−1.78065	−	2.45085i	−0.172142	−	0.236933i	0.714225	−	0.699916i	$-0.246779\pi$
$107$	−1.78065	−	2.45085i	−0.172142	−	0.236933i	−0.886367	+	0.462983i	$0.846779\pi$
$108$	1.06312	−	1.93380i	0.102298	−	0.186080i
$109$	−1.09503	+	1.72550i	−0.104885	+	0.165273i	−0.892717	−	0.450618i	$-0.851204\pi$
$109$	−1.09503	+	1.72550i	−0.104885	+	0.165273i	0.787832	+	0.615891i	$0.211204\pi$
$110$		0			0
$111$	−0.147484	−	0.0583932i	−0.0139986	−	0.00554244i
$112$	0.691855	+	1.74743i	0.0653742	+	0.165116i
$113$	9.87019	−	8.16533i	0.928509	−	0.768130i	−0.0444728	−	0.999011i	$-0.514161\pi$
$113$	9.87019	−	8.16533i	0.928509	−	0.768130i	0.972982	+	0.230881i	$0.0741608\pi$
$114$	0.715441	−	0.183694i	0.0670072	−	0.0172045i
$115$		0			0
$116$	2.65120	−	1.04968i	0.246158	−	0.0974607i
$117$	3.32122	+	3.53674i	0.307047	+	0.326972i
$118$	1.86908	−	2.57257i	0.172063	−	0.236824i
$119$	−4.90166	−	10.4166i	−0.449334	−	0.954884i
$120$		0			0
$121$	23.7755	−	13.0707i	2.16141	−	1.18825i
$122$	−6.95540	+	1.32681i	−0.629712	+	0.120124i
$123$	0.636734	+	2.47992i	0.0574124	+	0.223607i
$124$	10.5116			0.943970
$125$		0			0
$126$	11.0020			0.980136
$127$	−1.15736	−	4.50764i	−0.102700	−	0.399988i	0.896361	−	0.443325i	$-0.146201\pi$
$127$	−1.15736	−	4.50764i	−0.102700	−	0.399988i	−0.999061	+	0.0433367i	$0.986201\pi$
$128$	−5.16387	+	0.985060i	−0.456426	+	0.0870679i
$129$	1.82741	−	1.00463i	0.160894	−	0.0884524i
$130$		0			0
$131$	5.42110	+	11.5204i	0.473643	+	1.00654i	0.988772	+	0.149431i	$0.0477440\pi$
$131$	5.42110	+	11.5204i	0.473643	+	1.00654i	−0.515129	+	0.857113i	$0.672256\pi$
$132$	1.35983	−	1.87165i	0.118358	−	0.162906i
$133$	−6.68176	−	7.11536i	−0.579382	−	0.616980i
$134$	−4.09387	+	1.62088i	−0.353657	+	0.140023i
$135$		0			0
$136$	−7.97226	+	2.04693i	−0.683616	+	0.175523i
$137$	10.1637	−	8.40815i	0.868344	−	0.718357i	−0.0924211	−	0.995720i	$-0.529461\pi$
$137$	10.1637	−	8.40815i	0.868344	−	0.718357i	0.960765	+	0.277363i	$0.0894606\pi$
$138$	−0.406225	−	1.02601i	−0.0345802	−	0.0873396i
$139$	−0.502527	−	0.198964i	−0.0426238	−	0.0168759i	0.346716	−	0.937970i	$-0.387297\pi$
$139$	−0.502527	−	0.198964i	−0.0426238	−	0.0168759i	−0.389340	+	0.921094i	$0.627297\pi$
$140$		0			0
$141$	−0.901481	+	1.42051i	−0.0759184	+	0.119628i
$142$	−2.91025	+	5.29372i	−0.244223	+	0.444239i
$143$	6.09294	+	8.38622i	0.509518	+	0.701291i
$144$	0.249304	−	1.30690i	0.0207753	−	0.108908i
$145$		0			0
$146$	2.70119	−	5.74031i	0.223552	−	0.475072i
$147$	1.54338	+	2.80740i	0.127296	+	0.231551i
$148$	0.540182	+	0.0339854i	0.0444027	+	0.00279358i
$149$	2.22445	+	1.61616i	0.182234	+	0.132401i	0.675163	−	0.737669i	$-0.264073\pi$
$149$	2.22445	+	1.61616i	0.182234	+	0.132401i	−0.492928	+	0.870070i	$0.664073\pi$
$150$		0			0
$151$	4.40252	−	3.19862i	0.358272	−	0.260300i	−0.394059	−	0.919085i	$-0.628929\pi$
$151$	4.40252	−	3.19862i	0.358272	−	0.260300i	0.752331	+	0.658785i	$0.228929\pi$
$152$	−5.89230	+	3.73937i	−0.477929	+	0.303303i
$153$	−1.02143	+	8.08542i	−0.0825774	+	0.653667i
$154$	23.3210	+	2.94613i	1.87926	+	0.237406i
$155$		0			0
$156$	0.551122	+	0.302982i	0.0441251	+	0.0242580i
$157$	−15.0597	−	4.89318i	−1.20189	−	0.390518i	−0.361436	−	0.932397i	$-0.617713\pi$
$157$	−15.0597	−	4.89318i	−1.20189	−	0.390518i	−0.840457	+	0.541879i	$0.817713\pi$
$158$	10.5987	−	4.98737i	0.843187	−	0.396774i
$159$	2.02448	+	0.519797i	0.160551	+	0.0412226i
$160$		0			0
$161$	−9.29504	+	11.2358i	−0.732552	+	0.885503i
$162$	−6.31674	−	4.00872i	−0.496290	−	0.314955i
$163$	−4.40261	+	0.276989i	−0.344839	+	0.0216955i	−0.234266	−	0.972173i	$-0.575269\pi$
$163$	−4.40261	+	0.276989i	−0.344839	+	0.0216955i	−0.110573	+	0.993868i	$0.535269\pi$
$164$	−4.68117	−	7.37635i	−0.365538	−	0.575996i
$165$		0			0
$166$	−1.05308	−	16.7383i	−0.0817352	−	1.29914i
$167$	10.2844	+	1.96185i	0.795829	+	0.151813i	0.569233	−	0.822176i	$-0.307240\pi$
$167$	10.2844	+	1.96185i	0.795829	+	0.151813i	0.226596	+	0.973989i	$0.427240\pi$
$168$	3.75562	−	1.22028i	0.289752	−	0.0941463i
$169$	7.42240	−	6.97009i	0.570954	−	0.536161i
$170$		0			0
$171$	1.29478	+	6.78748i	0.0990144	+	0.519052i
$172$	−4.87094	+	5.18702i	−0.371406	+	0.395507i
$173$	−1.61183	+	4.07101i	−0.122545	+	0.309513i	−0.978079	−	0.208233i	$-0.933229\pi$
$173$	−1.61183	+	4.07101i	−0.122545	+	0.309513i	0.855534	+	0.517746i	$0.173229\pi$
$174$	0.240776	+	0.741033i	0.0182532	+	0.0561776i
$175$		0			0
$176$	0.878413	−	2.70348i	0.0662129	−	0.203782i
$177$	−0.870741	−	0.720340i	−0.0654489	−	0.0541441i
$178$	0.693356	+	0.326268i	0.0519692	+	0.0244549i
$179$	4.43446	+	4.16423i	0.331447	+	0.311249i	0.832346	−	0.554256i	$-0.186997\pi$
$179$	4.43446	+	4.16423i	0.331447	+	0.311249i	−0.500899	+	0.865506i	$0.666997\pi$
$180$		0			0
$181$	1.76787	−	0.223334i	0.131405	−	0.0166003i	−0.0593557	−	0.998237i	$-0.518905\pi$
$181$	1.76787	−	0.223334i	0.131405	−	0.0166003i	0.190761	+	0.981637i	$0.438905\pi$
$182$			6.39013i			0.473668i
$183$	0.315391	+	2.49658i	0.0233144	+	0.184553i
$184$	6.64565	+	8.03321i	0.489924	+	0.592216i
$185$		0			0
$186$	−0.180356	+	2.86667i	−0.0132243	+	0.210195i
$187$	−4.33025	+	16.8652i	−0.316659	+	1.23331i
$188$	1.42765	−	5.56032i	0.104122	−	0.405528i
$189$	0.500343	−	7.95272i	0.0363946	−	0.578475i
$190$		0			0
$191$	7.88201	+	9.52772i	0.570322	+	0.689401i	0.974271	−	0.225380i	$-0.0723625\pi$
$191$	7.88201	+	9.52772i	0.570322	+	0.689401i	−0.403948	+	0.914782i	$0.632362\pi$
$192$	−0.247675	−	1.96055i	−0.0178744	−	0.141491i
$193$			21.2332i			1.52840i	0.644980	+	0.764200i	$0.276866\pi$
$193$			21.2332i			1.52840i	−0.644980	+	0.764200i	$0.723134\pi$
$194$	−1.21742	+	0.153796i	−0.0874056	+	0.0110419i
$195$		0			0
$196$	−7.96870	−	7.48311i	−0.569193	−	0.534508i
$197$	10.7142	+	5.04173i	0.763357	+	0.359208i	0.767723	−	0.640782i	$-0.221390\pi$
$197$	10.7142	+	5.04173i	0.763357	+	0.359208i	−0.00436610	+	0.999990i	$0.501390\pi$
$198$	−12.8218	−	10.6071i	−0.911203	−	0.753813i
$199$	−1.46691	+	4.51468i	−0.103986	+	0.320037i	−0.989491	−	0.144593i	$-0.953813\pi$
$199$	−1.46691	+	4.51468i	−0.103986	+	0.320037i	0.885505	+	0.464630i	$0.153813\pi$
$200$		0			0
$201$	0.483547	+	1.48820i	0.0341067	+	0.104970i
$202$	2.99854	−	7.57345i	0.210977	−	0.532866i
$203$	7.04831	−	7.50569i	0.494695	−	0.526796i
$204$	0.197954	+	1.03771i	0.0138595	+	0.0726543i
$205$		0			0
$206$	−7.61055	+	7.14678i	−0.530252	+	0.497940i
$207$	9.81774	−	3.18998i	0.682380	−	0.221719i
$208$	0.759066	+	0.144800i	0.0526317	+	0.0100400i
$209$	0.926996	+	14.7342i	0.0641217	+	1.01918i
$210$		0			0
$211$	−5.39127	−	8.49528i	−0.371150	−	0.584839i	0.606498	−	0.795085i	$-0.292574\pi$
$211$	−5.39127	−	8.49528i	−0.371150	−	0.584839i	−0.977649	+	0.210246i	$0.932574\pi$
$212$	−7.11783	+	0.447816i	−0.488855	+	0.0307561i
$213$	1.81266	+	1.15035i	0.124201	+	0.0788206i
$214$	−1.80047	+	2.17639i	−0.123077	+	0.148775i
$215$		0			0
$216$	−5.51819	−	1.41683i	−0.375465	−	0.0964031i
$217$	34.3441	−	16.1611i	2.33143	−	1.09709i
$218$	1.81220	+	0.588821i	0.122738	+	0.0398800i
$219$	−1.97572	−	1.08616i	−0.133507	−	0.0733961i
$220$		0			0
$221$	−4.69614	−	0.593260i	−0.315896	−	0.0399070i
$222$	−0.0185367	+	0.146733i	−0.00124410	+	0.00984806i
$223$	−9.31883	+	5.91391i	−0.624035	+	0.396025i	−0.809915	−	0.586548i	$-0.800487\pi$
$223$	−9.31883	+	5.91391i	−0.624035	+	0.396025i	0.185879	+	0.982573i	$0.440487\pi$
$224$	−17.8649	+	12.9796i	−1.19365	+	0.867238i
$225$		0			0
$226$	−9.66275	−	7.02040i	−0.642756	−	0.466990i
$227$	−10.0752	−	0.633880i	−0.668717	−	0.0420721i	−0.275196	−	0.961388i	$-0.588743\pi$
$227$	−10.0752	−	0.633880i	−0.668717	−	0.0420721i	−0.393520	+	0.919316i	$0.628743\pi$
$228$	0.431511	+	0.784916i	0.0285775	+	0.0519823i
$229$	9.84627	−	20.9244i	0.650660	−	1.38272i	−0.258392	−	0.966040i	$-0.583193\pi$
$229$	9.84627	−	20.9244i	0.650660	−	1.38272i	0.909052	−	0.416682i	$-0.136807\pi$
$230$		0			0
$231$	1.56535	−	8.20586i	0.102993	−	0.539906i
$232$	−4.32700	−	5.95560i	−0.284081	−	0.391004i
$233$	7.93497	−	14.4337i	0.519837	−	0.945581i	−0.477904	−	0.878412i	$-0.658603\pi$
$233$	7.93497	−	14.4337i	0.519837	−	0.945581i	0.997742	−	0.0671688i	$-0.0213966\pi$
$234$	2.42391	−	3.81947i	0.158456	−	0.249687i
$235$		0			0
$236$	3.58524	+	1.41950i	0.233379	+	0.0924013i
$237$	−1.53243	−	3.87048i	−0.0995422	−	0.251415i
$238$	−8.27058	+	6.84202i	−0.536102	+	0.443502i
$239$	−12.2857	+	3.15444i	−0.794698	+	0.204044i	−0.624149	−	0.781305i	$-0.714554\pi$
$239$	−12.2857	+	3.15444i	−0.794698	+	0.204044i	−0.170549	+	0.985349i	$0.554554\pi$
$240$		0			0
$241$	12.9735	−	5.13657i	0.835696	−	0.330876i	0.0889926	−	0.996032i	$-0.471635\pi$
$241$	12.9735	−	5.13657i	0.835696	−	0.330876i	0.746704	+	0.665157i	$0.231635\pi$
$242$	−17.3171	−	18.4408i	−1.11319	−	1.18542i
$243$	−5.00445	+	6.88803i	−0.321035	+	0.441867i
$244$	−3.65593	−	7.76925i	−0.234047	−	0.497376i
$245$		0			0
$246$	2.09196	−	1.15007i	0.133379	−	0.0733255i
$247$	−3.94227	+	0.752029i	−0.250841	+	0.0478505i
$248$	−6.74887	−	26.2851i	−0.428554	−	1.66911i
$249$	−5.96031			−0.377720
$250$		0			0
$251$	6.38750			0.403175			0.201588	−	0.979470i	$-0.435390\pi$
$251$	6.38750			0.403175			0.201588	+	0.979470i	$0.435390\pi$
$252$	3.31787	+	12.9223i	0.209006	+	0.814026i
$253$	21.6649	−	4.13281i	1.36206	−	0.259827i
$254$	−3.80247	+	2.09043i	−0.238588	+	0.131165i
$255$		0			0
$256$	7.16546	+	15.2274i	0.447841	+	0.951711i
$257$	−7.66022	+	10.5434i	−0.477831	+	0.657679i	−0.978086	−	0.208200i	$-0.933240\pi$
$257$	−7.66022	+	10.5434i	−0.477831	+	0.657679i	0.500255	+	0.865878i	$0.333240\pi$
$258$	−1.33101	−	1.41738i	−0.0828648	−	0.0882421i
$259$	1.81717	−	0.719467i	0.112913	−	0.0447055i
$260$		0			0
$261$	−7.05994	+	1.81268i	−0.436999	+	0.112202i
$262$	9.14703	−	7.56708i	0.565106	−	0.467496i
$263$	0.581810	+	1.46948i	0.0358759	+	0.0906123i	0.946610	−	0.322381i	$-0.104483\pi$
$263$	0.581810	+	1.46948i	0.0358759	+	0.0906123i	−0.910734	+	0.412993i	$0.864483\pi$
$264$	−5.55329	−	2.19870i	−0.341781	−	0.135321i
$265$		0			0
$266$	−4.87652	+	7.68416i	−0.298999	+	0.471146i
$267$	0.131194	−	0.238642i	0.00802897	−	0.0146046i
$268$	−3.13837	−	4.31960i	−0.191707	−	0.263862i
$269$	−0.0471816	+	0.247335i	−0.00287672	+	0.0150803i	−0.983697	−	0.179836i	$-0.942443\pi$
$269$	−0.0471816	+	0.247335i	−0.00287672	+	0.0150803i	0.980820	+	0.194916i	$0.0624434\pi$
$270$		0			0
$271$	−4.48654	+	9.53439i	−0.272538	+	0.579173i	−0.993504	−	0.113798i	$-0.963698\pi$
$271$	−4.48654	+	9.53439i	−0.272538	+	0.579173i	0.720966	+	0.692971i	$0.243698\pi$
$272$	0.625334	+	1.13748i	0.0379164	+	0.0689698i
$273$	2.26648	+	0.142595i	0.137174	+	0.00863024i
$274$	−9.95010	−	7.22917i	−0.601107	−	0.436730i
$275$		0			0
$276$	1.08258	−	0.786540i	0.0651636	−	0.0473441i
$277$	4.27478	−	2.71286i	0.256847	−	0.163000i	−0.401169	−	0.916004i	$-0.631396\pi$
$277$	4.27478	−	2.71286i	0.256847	−	0.163000i	0.658016	+	0.753004i	$0.271396\pi$
$278$	−0.0631603	+	0.499966i	−0.00378811	+	0.0299859i
$279$	−26.6582	−	3.36772i	−1.59599	−	0.201620i
$280$		0			0
$281$	−24.7342	−	13.5978i	−1.47552	−	0.811174i	−0.477787	−	0.878475i	$-0.658561\pi$
$281$	−24.7342	−	13.5978i	−1.47552	−	0.811174i	−0.997733	+	0.0673014i	$0.978561\pi$
$282$	1.49189	+	0.484744i	0.0888407	+	0.0288661i
$283$	−29.8457	+	14.0443i	−1.77415	+	0.834849i	−0.803140	+	0.595790i	$0.796839\pi$
$283$	−29.8457	+	14.0443i	−1.77415	+	0.834849i	−0.971005	+	0.239059i	$0.923161\pi$
$284$	−7.09532	−	1.82177i	−0.421030	−	0.108102i
$285$		0			0
$286$	6.16076	−	7.44708i	0.364294	−	0.440355i
$287$	−26.6354	−	16.9034i	−1.57224	−	0.997773i
$288$	15.6016	−	0.981567i	0.919331	−	0.0578394i
$289$	4.84866	+	7.64027i	0.285216	+	0.449428i
$290$		0			0
$291$	0.0273824	+	0.435231i	0.00160519	+	0.0255137i
$292$	7.55681	+	1.44154i	0.442229	+	0.0843597i
$293$	−5.63000	+	1.82930i	−0.328908	+	0.106869i	−0.468816	−	0.883296i	$-0.655319\pi$
$293$	−5.63000	+	1.82930i	−0.328908	+	0.106869i	0.139908	+	0.990164i	$0.455319\pi$
$294$	2.17748	−	2.04479i	0.126993	−	0.119255i
$295$		0			0
$296$	−0.261835	−	1.37259i	−0.0152189	−	0.0797801i
$297$	−8.25036	+	8.78575i	−0.478735	+	0.509801i
$298$	0.943752	−	2.38365i	0.0546701	−	0.138081i
$299$	1.85279	+	5.70229i	0.107149	+	0.329772i
$300$		0			0
$301$	−7.93981	+	24.4362i	−0.457643	+	1.40848i
$302$	−3.90950	−	3.23422i	−0.224967	−	0.186109i
$303$	−2.61927	−	1.23254i	−0.150473	−	0.0708074i
$304$	0.802279	+	0.753390i	0.0460138	+	0.0432099i
$305$		0			0
$306$	7.53876	−	0.952367i	0.430963	−	0.0544432i
$307$			14.7323i			0.840819i	0.907335	+	0.420409i	$0.138114\pi$
$307$			14.7323i			0.840819i	−0.907335	+	0.420409i	$0.861886\pi$
$308$	3.57258	+	28.2799i	0.203567	+	1.61140i
$309$	2.36502	+	2.85882i	0.134542	+	0.162633i
$310$		0			0
$311$	0.562061	−	8.93371i	0.0318716	−	0.506584i	−0.949414	−	0.314027i	$-0.898322\pi$
$311$	0.562061	−	8.93371i	0.0318716	−	0.506584i	0.981286	−	0.192557i	$-0.0616782\pi$
$312$	0.403789	−	1.57265i	0.0228600	−	0.0890339i
$313$	3.66490	−	14.2739i	0.207152	−	0.806806i	−0.777003	−	0.629497i	$-0.783261\pi$
$313$	3.66490	−	14.2739i	0.207152	−	0.806806i	0.984155	−	0.177309i	$-0.0567391\pi$
$314$	−0.927045	+	14.7350i	−0.0523162	+	0.831542i
$315$		0			0
$316$	9.05410	+	10.9445i	0.509333	+	0.615678i
$317$	3.49578	+	27.6720i	0.196343	+	1.55421i	0.714935	+	0.699191i	$0.246456\pi$
$317$	3.49578	+	27.6720i	0.196343	+	1.55421i	−0.518592	+	0.855022i	$0.673544\pi$
$318$		−	1.94883i		−	0.109285i
$319$	−15.4504	+	1.95184i	−0.865057	+	0.109282i
$320$		0			0
$321$	0.731755	+	0.687164i	0.0408426	+	0.0383537i
$322$	12.3023	+	5.78902i	0.685580	+	0.322609i
$323$	−5.19439	−	4.29717i	−0.289024	−	0.239101i
$324$	2.80346	−	8.62816i	0.155748	−	0.479342i
$325$		0			0
$326$	1.27101	+	3.91176i	0.0703947	+	0.216652i
$327$	0.249285	−	0.629621i	0.0137855	−	0.0348181i
$328$	−15.4397	+	16.4416i	−0.852513	+	0.907834i
$329$	−3.88425	−	20.3619i	−0.214146	−	1.12259i
$330$		0			0
$331$	−6.06326	+	5.69378i	−0.333267	+	0.312958i	−0.833056	−	0.553189i	$-0.813411\pi$
$331$	−6.06326	+	5.69378i	−0.333267	+	0.312958i	0.499789	+	0.866147i	$0.333411\pi$
$332$	19.3422	−	6.28466i	1.06154	−	0.344915i
$333$	−1.35905	−	0.259254i	−0.0744757	−	0.0142070i
$334$	−0.612959	−	9.74270i	−0.0335396	−	0.533097i
$335$		0			0
$336$	−0.333689	−	0.525810i	−0.0182042	−	0.0286853i
$337$	24.9066	−	1.56699i	1.35675	−	0.0853594i	0.632319	−	0.774708i	$-0.282103\pi$
$337$	24.9066	−	1.56699i	1.35675	−	0.0853594i	0.724430	+	0.689348i	$0.242103\pi$
$338$	−8.01575	−	5.08695i	−0.435999	−	0.276694i
$339$	−2.70565	+	3.27057i	−0.146951	+	0.177633i
$340$		0			0
$341$	−55.6058	−	14.2771i	−3.01122	−	0.773151i
$342$	5.82953	−	2.74317i	0.315225	−	0.148333i
$343$	−10.3607	−	3.36641i	−0.559427	−	0.181769i
$344$	16.0979	+	8.84991i	0.867942	+	0.477155i
$345$		0			0
$346$	4.05026	+	0.511667i	0.217744	+	0.0275074i
$347$	2.89344	−	22.9039i	0.155328	−	1.22955i	−0.701018	−	0.713143i	$-0.747271\pi$
$347$	2.89344	−	22.9039i	0.155328	−	1.22955i	0.856346	−	0.516402i	$-0.172729\pi$
$348$	−0.797760	+	0.506274i	−0.0427644	+	0.0271391i
$349$	6.00930	−	4.36601i	0.321670	−	0.233707i	−0.415218	−	0.909722i	$-0.636295\pi$
$349$	6.00930	−	4.36601i	0.321670	−	0.233707i	0.736888	+	0.676015i	$0.236295\pi$
$350$		0			0
$351$	−2.65065	−	1.92581i	−0.141481	−	0.102792i
$352$	33.3336	+	2.09717i	1.77669	+	0.111780i
$353$	−3.88082	−	7.05918i	−0.206555	−	0.375722i	0.752656	−	0.658414i	$-0.228773\pi$
$353$	−3.88082	−	7.05918i	−0.206555	−	0.375722i	−0.959211	+	0.282692i	$0.908773\pi$
$354$	−0.448633	+	0.953394i	−0.0238446	+	0.0506723i
$355$		0			0
$356$	−0.174119	+	0.912765i	−0.00922831	+	0.0483765i
$357$	2.24220	+	3.08613i	0.118670	+	0.163335i
$358$	2.73246	−	4.97033i	0.144415	−	0.262690i
$359$	−12.3113	+	19.3995i	−0.649765	+	1.02387i	0.346544	+	0.938034i	$0.387355\pi$
$359$	−12.3113	+	19.3995i	−0.649765	+	1.02387i	−0.996310	+	0.0858326i	$0.972645\pi$
$360$		0			0
$361$	12.3513	+	4.89021i	0.650066	+	0.257379i
$362$	−0.611619	−	1.54477i	−0.0321460	−	0.0811915i
$363$	−6.92710	+	5.73060i	−0.363579	+	0.300778i
$364$	−7.50546	+	1.92707i	−0.393393	+	0.101006i
$365$		0			0
$366$	2.18152	−	0.863726i	0.114030	−	0.0451477i
$367$	−11.3523	−	12.0890i	−0.592586	−	0.631040i	0.360854	−	0.932622i	$-0.382485\pi$
$367$	−11.3523	−	12.0890i	−0.592586	−	0.631040i	−0.953440	+	0.301582i	$0.902485\pi$
$368$	0.966429	−	1.33018i	0.0503786	−	0.0693402i
$369$	9.50857	+	20.2067i	0.494996	+	1.05192i
$370$		0			0
$371$	−22.5673	+	12.4065i	−1.17164	+	0.644113i
$372$	−3.42141	+	0.652669i	−0.177392	+	0.0338393i
$373$	3.98138	+	15.5065i	0.206148	+	0.802895i	0.984546	+	0.175124i	$0.0560325\pi$
$373$	3.98138	+	15.5065i	0.206148	+	0.802895i	−0.778398	+	0.627771i	$0.783967\pi$
$374$	16.2350			0.839492
$375$		0			0
$376$	−14.8206			−0.764316
$377$	−1.05284	−	4.10052i	−0.0542238	−	0.211188i
$378$	−7.29810	+	1.39219i	−0.375374	+	0.0716064i
$379$	−32.0491	+	17.6191i	−1.64625	+	0.905034i	−0.657853	+	0.753146i	$0.728535\pi$
$379$	−32.0491	+	17.6191i	−1.64625	+	0.905034i	−0.988398	+	0.151888i	$0.951465\pi$
$380$		0			0
$381$	0.656590	+	1.39532i	0.0336381	+	0.0714846i
$382$	6.77681	−	9.32747i	0.346732	−	0.477235i
$383$	−6.77689	−	7.21665i	−0.346283	−	0.368754i	0.532125	−	0.846666i	$-0.321394\pi$
$383$	−6.77689	−	7.21665i	−0.346283	−	0.368754i	−0.878408	+	0.477912i	$0.841394\pi$
$384$	1.61962	−	0.641252i	0.0826508	−	0.0327238i
$385$		0			0
$386$	19.1756	−	4.92347i	0.976015	−	0.250598i
$387$	14.0149	−	11.5941i	0.712417	−	0.589363i
$388$	−0.547776	−	1.38352i	−0.0278091	−	0.0702378i
$389$	−0.681310	−	0.269750i	−0.0345438	−	0.0136768i	0.350789	−	0.936454i	$-0.385913\pi$
$389$	−0.681310	−	0.269750i	−0.0345438	−	0.0136768i	−0.385333	+	0.922778i	$0.625913\pi$
$390$		0			0
$391$	−5.39652	+	8.50355i	−0.272914	+	0.430043i
$392$	−13.5959	+	24.7309i	−0.686697	+	1.24910i
$393$	−2.47981	−	3.41317i	−0.125090	−	0.172172i
$394$	2.06880	−	10.8450i	0.104225	−	0.546365i
$395$		0			0
$396$	8.59177	−	18.2584i	0.431753	−	0.917521i
$397$	−10.4578	−	19.0227i	−0.524862	−	0.954721i	−0.997306	−	0.0733600i	$-0.976628\pi$
$397$	−10.4578	−	19.0227i	−0.524862	−	0.954721i	0.472443	−	0.881361i	$-0.343372\pi$
$398$	4.41733	+	0.277915i	0.221421	+	0.0139306i
$399$	2.61663	+	1.90110i	0.130996	+	0.0951738i
$400$		0			0
$401$	25.6920	−	18.6663i	1.28300	−	0.932152i	0.283358	−	0.959014i	$-0.408552\pi$
$401$	25.6920	−	18.6663i	1.28300	−	0.932152i	0.999639	+	0.0268626i	$0.00855166\pi$
$402$	1.23187	−	0.781768i	0.0614401	−	0.0389911i
$403$	1.95602	−	15.4835i	0.0974364	−	0.771289i
$404$	9.79958	+	1.23797i	0.487547	+	0.0615915i
$405$		0			0
$406$	−8.41271	−	4.62492i	−0.417516	−	0.229531i
$407$	−2.81137	−	0.913471i	−0.139355	−	0.0452791i
$408$	2.46779	−	1.16125i	0.122174	−	0.0574906i
$409$	19.4632	+	4.99730i	0.962393	+	0.247101i	0.697025	−	0.717047i	$-0.254507\pi$
$409$	19.4632	+	4.99730i	0.962393	+	0.247101i	0.265368	+	0.964147i	$0.414507\pi$
$410$		0			0
$411$	−2.78611	+	3.36783i	−0.137429	+	0.166123i
$412$	−10.6893	−	6.78362i	−0.526623	−	0.334205i
$413$	13.8963	−	0.874282i	0.683793	−	0.0430206i
$414$	−5.15736	−	8.12669i	−0.253470	−	0.399405i
$415$		0			0
$416$	0.570109	+	9.06163i	0.0279519	+	0.444283i
$417$	0.175921	+	0.0335586i	0.00861487	+	0.00164337i
$418$	13.0915	−	4.25367i	0.640324	−	0.208054i
$419$	6.05387	−	5.68496i	0.295751	−	0.277728i	−0.522439	−	0.852677i	$-0.674978\pi$
$419$	6.05387	−	5.68496i	0.295751	−	0.277728i	0.818190	+	0.574948i	$0.194978\pi$
$420$		0			0
$421$	−4.00752	−	21.0082i	−0.195315	−	1.02388i	−0.935994	−	0.352016i	$-0.885496\pi$
$421$	−4.00752	−	21.0082i	−0.195315	−	1.02388i	0.740679	−	0.671859i	$-0.234504\pi$
$422$	−6.42196	+	6.83869i	−0.312616	+	0.332902i
$423$	−5.40204	+	13.6440i	−0.262656	+	0.663394i
$424$	5.68974	+	17.5112i	0.276318	+	0.850420i
$425$		0			0
$426$	0.618564	−	1.90375i	0.0299695	−	0.0922368i
$427$	−23.8898	−	19.7633i	−1.15611	−	0.956415i
$428$	−3.09922	−	1.45838i	−0.149807	−	0.0704936i
$429$	−2.50389	−	2.35131i	−0.120889	−	0.113522i
$430$		0			0
$431$	4.50434	−	0.569031i	0.216967	−	0.0274092i	−0.0160984	−	0.999870i	$-0.505125\pi$
$431$	4.50434	−	0.569031i	0.216967	−	0.0274092i	0.233065	+	0.972461i	$0.425125\pi$
$432$			0.898467i			0.0432275i
$433$	−2.63506	−	20.8587i	−0.126633	−	1.00240i	−0.919522	−	0.393038i	$-0.871424\pi$
$433$	−2.63506	−	20.8587i	−0.126633	−	1.00240i	0.792889	−	0.609366i	$-0.208576\pi$
$434$	−22.5586	−	27.2687i	−1.08285	−	1.30894i
$435$		0			0
$436$	−0.145086	+	2.30607i	−0.00694835	+	0.110441i
$437$	−2.12362	+	8.27095i	−0.101587	+	0.395653i
$438$	−0.522788	+	2.03613i	−0.0249798	+	0.0972898i
$439$	2.01157	−	31.9730i	0.0960071	−	1.52599i	−0.595344	−	0.803471i	$-0.702984\pi$
$439$	2.01157	−	31.9730i	0.0960071	−	1.52599i	0.691351	−	0.722519i	$-0.257016\pi$
$440$		0			0
$441$	17.8118	+	21.5308i	0.848181	+	1.02527i
$442$	0.553150	+	4.37863i	0.0263107	+	0.208270i
$443$		−	8.33622i		−	0.396066i	−0.980195	−	0.198033i	$-0.936545\pi$
$443$		−	8.33622i		−	0.396066i	0.980195	−	0.198033i	$-0.0634553\pi$
$444$	−0.177933	+	0.0224782i	−0.00844434	+	0.00106677i
$445$		0			0
$446$	7.50165	+	7.04452i	0.355213	+	0.333568i
$447$	−0.824382	−	0.387925i	−0.0389919	−	0.0183482i
$448$	18.7605	+	15.5201i	0.886352	+	0.733254i
$449$	7.01672	−	21.5952i	0.331139	−	1.01914i	−0.637453	−	0.770489i	$-0.720012\pi$
$449$	7.01672	−	21.5952i	0.331139	−	1.01914i	0.968593	−	0.248653i	$-0.0799879\pi$
$450$		0			0
$451$	14.7444	+	45.3786i	0.694286	+	2.13679i
$452$	5.33173	−	13.4664i	0.250783	−	0.633406i
$453$	−1.23437	+	1.31447i	−0.0579957	+	0.0617591i
$454$	1.76375	+	9.24590i	0.0827768	+	0.433931i
$455$		0			0
$456$	1.68570	−	1.58298i	0.0789401	−	0.0741297i
$457$	0.690128	−	0.224236i	0.0322828	−	0.0104893i	−0.292831	−	0.956164i	$-0.594597\pi$
$457$	0.690128	−	0.224236i	0.0322828	−	0.0104893i	0.325114	+	0.945675i	$0.394597\pi$
$458$	−21.1799	−	4.04028i	−0.989670	−	0.188790i
$459$	−0.345569	−	5.49266i	−0.0161298	−	0.256375i
$460$		0			0
$461$	−4.96592	−	7.82504i	−0.231286	−	0.364449i	0.708786	−	0.705423i	$-0.249243\pi$
$461$	−4.96592	−	7.82504i	−0.231286	−	0.364449i	−0.940073	+	0.340975i	$0.889243\pi$
$462$	−7.77366	+	0.489077i	−0.361663	+	0.0227539i
$463$	−22.2047	−	14.0915i	−1.03194	−	0.654890i	−0.0918359	−	0.995774i	$-0.529274\pi$
$463$	−22.2047	−	14.0915i	−1.03194	−	0.654890i	−0.940105	+	0.340884i	$0.889274\pi$
$464$	−0.740012	+	0.894521i	−0.0343542	+	0.0415271i
$465$		0			0
$466$	−14.8749	−	3.81923i	−0.689068	−	0.176923i
$467$	−12.3605	+	5.81641i	−0.571976	+	0.269151i	−0.689940	−	0.723866i	$-0.742363\pi$
$467$	−12.3605	+	5.81641i	−0.571976	+	0.269151i	0.117964	+	0.993018i	$0.462363\pi$
$468$	5.21709	+	1.69514i	0.241160	+	0.0783577i
$469$	−16.8951	−	9.28815i	−0.780143	−	0.428887i
$470$		0			0
$471$	5.20557	+	0.657617i	0.239860	+	0.0303014i
$472$	1.24770	−	9.87655i	0.0574300	−	0.454605i
$473$	32.8122	−	20.8232i	1.50870	−	0.957453i
$474$	−3.14009	+	2.28141i	−0.144229	+	0.104789i
$475$		0			0
$476$	−10.5304	−	7.65077i	−0.482659	−	0.350672i
$477$	18.1948	+	1.14472i	0.833085	+	0.0524132i
$478$	5.69753	+	10.3638i	0.260599	+	0.474028i
$479$	−3.75425	+	7.97819i	−0.171536	+	0.364533i	−0.972047	−	0.234785i	$-0.924561\pi$
$479$	−3.75425	+	7.97819i	−0.171536	+	0.364533i	0.800511	+	0.599318i	$0.204561\pi$
$480$		0			0
$481$	0.150578	−	0.789360i	0.00686579	−	0.0359917i
$482$	−7.64707	−	10.5253i	−0.348314	−	0.479414i
$483$	2.32780	−	4.23425i	0.105918	−	0.192665i
$484$	16.4371	−	25.9008i	0.747143	−	1.17731i
$485$		0			0
$486$	7.38097	+	2.92233i	0.334808	+	0.132560i
$487$	14.2069	+	35.8826i	0.643778	+	1.62600i	0.773018	+	0.634384i	$0.218746\pi$
$487$	14.2069	+	35.8826i	0.643778	+	1.62600i	−0.129240	+	0.991613i	$0.541254\pi$
$488$	−17.0804	+	14.1301i	−0.773194	+	0.639641i
$489$	1.41580	−	0.363517i	0.0640248	−	0.0164388i
$490$		0			0
$491$	18.8271	−	7.45419i	0.849657	−	0.336403i	0.0973780	−	0.995247i	$-0.468954\pi$
$491$	18.8271	−	7.45419i	0.849657	−	0.336403i	0.752279	+	0.658844i	$0.228954\pi$
$492$	1.98167	+	2.11026i	0.0893405	+	0.0951380i
$493$	4.17991	−	5.75316i	0.188254	−	0.259109i
$494$	1.59327	+	3.38588i	0.0716848	+	0.152338i
$495$		0			0
$496$	−3.75035	+	2.06177i	−0.168396	+	0.0925763i
$497$	−25.9832	+	4.95655i	−1.16550	+	0.222332i
$498$	1.38205	+	5.38274i	0.0619313	+	0.241207i
$499$	−31.3155			−1.40187			−0.700936	−	0.713224i	$-0.747234\pi$
$499$	−31.3155			−1.40187			−0.700936	+	0.713224i	$0.747234\pi$
$500$		0			0
$501$	−3.46926			−0.154995
$502$	−1.48111	−	5.76853i	−0.0661051	−	0.257462i
$503$	5.99471	−	1.14355i	0.267291	−	0.0509885i	−0.0519934	−	0.998647i	$-0.516557\pi$
$503$	5.99471	−	1.14355i	0.267291	−	0.0509885i	0.319284	+	0.947659i	$0.396557\pi$
$504$	30.1830	−	16.5932i	1.34446	−	0.739122i
$505$		0			0
$506$	−8.75590	−	18.6072i	−0.389247	−	0.827193i
$507$	−1.98313	+	2.72955i	−0.0880740	+	0.121223i
$508$	−3.60200	−	3.83574i	−0.159813	−	0.170183i
$509$	6.80668	−	2.69495i	0.301701	−	0.119452i	−0.212397	−	0.977183i	$-0.568127\pi$
$509$	6.80668	−	2.69495i	0.301701	−	0.119452i	0.514097	+	0.857732i	$0.328127\pi$
$510$		0			0
$511$	26.9064	−	6.90838i	1.19027	−	0.305609i
$512$	3.98915	−	3.30012i	0.176297	−	0.145846i
$513$	−1.71777	−	4.33859i	−0.0758413	−	0.191553i
$514$	11.2979	+	4.47317i	0.498330	+	0.197303i
$515$		0			0
$516$	1.26337	−	1.99076i	0.0556169	−	0.0876382i
$517$	−15.1043	+	27.4747i	−0.664288	+	1.20834i
$518$	−1.07111	−	1.47425i	−0.0470617	−	0.0647749i
$519$	0.271862	−	1.42515i	0.0119334	−	0.0625571i
$520$		0			0
$521$	−11.7973	+	25.0706i	−0.516851	+	1.09836i	0.460679	+	0.887567i	$0.347606\pi$
$521$	−11.7973	+	25.0706i	−0.516851	+	1.09836i	−0.977530	+	0.210797i	$0.932394\pi$
$522$	3.27406	+	5.95550i	0.143302	+	0.260665i
$523$	6.50977	+	0.409560i	0.284652	+	0.0179088i	0.204475	−	0.978872i	$-0.434451\pi$
$523$	6.50977	+	0.409560i	0.284652	+	0.0179088i	0.0801774	+	0.996781i	$0.474451\pi$
$524$	11.6463	+	8.46153i	0.508771	+	0.369644i
$525$		0			0
$526$	1.19218	−	0.866169i	0.0519815	−	0.0377668i
$527$	22.1342	−	14.0468i	0.964183	−	0.611889i
$528$	−0.118054	+	0.934493i	−0.00513764	+	0.0406686i
$529$	−10.1621	−	1.28377i	−0.441830	−	0.0558161i
$530$		0			0
$531$	−8.63765	−	4.74859i	−0.374842	−	0.206071i
$532$	−10.4960	−	3.41034i	−0.455057	−	0.147857i
$533$	−11.7364	+	5.52273i	−0.508360	+	0.239216i
$534$	−0.245938	−	0.0631461i	−0.0106428	−	0.00273260i
$535$		0			0
$536$	−8.78656	+	10.6211i	−0.379521	+	0.458763i
$537$	−1.70192	−	1.08007i	−0.0734434	−	0.0466086i
$538$	0.234308	−	0.0147414i	0.0101017	−	0.000635547i
$539$	31.9902	+	50.4086i	1.37792	+	2.17125i
$540$		0			0
$541$	0.578883	+	9.20109i	0.0248881	+	0.395586i	0.990675	+	0.136248i	$0.0435043\pi$
$541$	0.578883	+	9.20109i	0.0248881	+	0.395586i	−0.965787	+	0.259338i	$0.916496\pi$
$542$	9.65080	+	1.84099i	0.414537	+	0.0790772i
$543$	−0.561556	+	0.182460i	−0.0240987	+	0.00783013i
$544$	−11.1178	+	10.4403i	−0.476672	+	0.447625i
$545$		0			0
$546$	−0.396765	−	2.07992i	−0.0169800	−	0.0890122i
$547$	8.42266	−	8.96922i	0.360127	−	0.383496i	−0.523235	−	0.852189i	$-0.675275\pi$
$547$	8.42266	−	8.96922i	0.360127	−	0.383496i	0.883361	+	0.468693i	$0.155275\pi$
$548$	5.49028	−	13.8669i	0.234533	−	0.592363i
$549$	6.78261	+	20.8747i	0.289475	+	0.890911i
$550$		0			0
$551$	1.86320	−	5.73435i	0.0793751	−	0.244292i
$552$	−2.66187	−	2.20209i	−0.113297	−	0.0937271i
$553$	46.4088	+	21.8383i	1.97351	+	0.928661i
$554$	−3.44119	−	3.23150i	−0.146202	−	0.137293i
$555$		0			0
$556$	−0.606276	+	0.0765904i	−0.0257118	+	0.00324816i
$557$			23.5217i			0.996647i	0.866991	+	0.498323i	$0.166051\pi$
$557$			23.5217i			0.996647i	−0.866991	+	0.498323i	$0.833949\pi$
$558$	3.14003	+	24.8559i	0.132928	+	1.05223i
$559$	6.73405	+	8.14007i	0.284820	+	0.344288i
$560$		0			0
$561$	0.362282	−	5.75830i	0.0152955	−	0.243116i
$562$	−6.54482	+	25.4904i	−0.276077	+	1.07525i
$563$	3.65062	−	14.2182i	0.153855	−	0.599227i	−0.844150	−	0.536106i	$-0.819895\pi$
$563$	3.65062	−	14.2182i	0.153855	−	0.599227i	0.998006	−	0.0631209i	$-0.0201054\pi$
$564$	−0.119441	+	1.89846i	−0.00502938	+	0.0799397i
$565$		0			0
$566$	19.6039	+	23.6971i	0.824014	+	0.996062i
$567$	−4.10578	−	32.5006i	−0.172427	−	1.36490i
$568$			18.9121i			0.793533i
$569$	33.0889	−	4.18010i	1.38716	−	0.175239i	0.603963	−	0.797012i	$-0.293587\pi$
$569$	33.0889	−	4.18010i	1.38716	−	0.175239i	0.783197	+	0.621773i	$0.213587\pi$
$570$		0			0
$571$	−0.312300	−	0.293269i	−0.0130693	−	0.0122729i	0.677985	−	0.735076i	$-0.262853\pi$
$571$	−0.312300	−	0.293269i	−0.0130693	−	0.0122729i	−0.691054	+	0.722803i	$0.742853\pi$
$572$	10.6048	+	4.99023i	0.443408	+	0.208652i
$573$	−3.15709	−	2.61177i	−0.131889	−	0.109108i
$574$	−9.08926	+	27.9739i	−0.379378	+	1.16761i
$575$		0			0
$576$	−5.32635	−	16.3928i	−0.221931	−	0.683034i
$577$	−14.9516	+	37.7635i	−0.622444	+	1.57211i	0.185365	+	0.982670i	$0.440653\pi$
$577$	−14.9516	+	37.7635i	−0.622444	+	1.57211i	−0.807809	+	0.589444i	$0.799347\pi$
$578$	5.77562	−	6.15041i	0.240234	−	0.255823i
$579$	−1.31838	−	6.91117i	−0.0547898	−	0.287218i
$580$		0			0
$581$	53.5336	−	50.2714i	2.22095	−	2.08561i
$582$	0.386707	−	0.125649i	0.0160295	−	0.00520831i
$583$	38.2612	+	7.29871i	1.58462	+	0.302282i
$584$	−1.24709	−	19.8220i	−0.0516050	−	0.820238i
$585$		0			0
$586$	2.95749	+	4.66027i	0.122173	+	0.192514i
$587$	−28.2978	+	1.78035i	−1.16798	+	0.0734829i	−0.634907	−	0.772589i	$-0.718962\pi$
$587$	−28.2978	+	1.78035i	−1.16798	+	0.0734829i	−0.533070	+	0.846071i	$0.678962\pi$
$588$	3.05835	+	1.94089i	0.126124	+	0.0800409i
$589$	14.1681	−	17.1263i	0.583786	−	0.705676i
$590$		0			0
$591$	−3.80040	−	0.975777i	−0.156328	−	0.0401381i
$592$	−0.199393	+	0.0938273i	−0.00819501	+	0.00385628i
$593$	8.03559	+	2.61092i	0.329982	+	0.107218i	0.469323	−	0.883027i	$-0.344498\pi$
$593$	8.03559	+	2.61092i	0.329982	+	0.107218i	−0.139340	+	0.990245i	$0.544498\pi$
$594$	9.84744	+	5.41368i	0.404046	+	0.222126i
$595$		0			0
$596$	3.08429	+	0.389636i	0.126337	+	0.0159601i
$597$	0.197144	−	1.56056i	0.00806858	−	0.0638694i
$598$	4.72011	−	2.99547i	0.193020	−	0.122494i
$599$	−14.7042	+	10.6832i	−0.600798	+	0.436505i	−0.846162	−	0.532926i	$-0.821092\pi$
$599$	−14.7042	+	10.6832i	−0.600798	+	0.436505i	0.245364	+	0.969431i	$0.421092\pi$
$600$		0			0
$601$	−30.4496	−	22.1229i	−1.24206	−	0.902412i	−0.244329	−	0.969692i	$-0.578568\pi$
$601$	−30.4496	−	22.1229i	−1.24206	−	0.902412i	−0.997734	+	0.0672805i	$0.978568\pi$
$602$	23.9093	+	1.50425i	0.974472	+	0.0613086i
$603$	6.57524	+	11.9603i	0.267764	+	0.487062i
$604$	2.61973	−	5.56720i	0.106595	−	0.226526i
$605$		0			0
$606$	−0.505754	+	2.65125i	−0.0205448	+	0.107700i
$607$	16.2757	+	22.4015i	0.660609	+	0.909250i	0.999501	−	0.0315753i	$-0.0100524\pi$
$607$	16.2757	+	22.4015i	0.660609	+	0.909250i	−0.338893	+	0.940825i	$0.610052\pi$
$608$	−6.22966	+	11.3317i	−0.252646	+	0.459562i
$609$	−1.82812	+	2.88065i	−0.0740790	+	0.116730i
$610$		0			0
$611$	−7.92465	−	3.13759i	−0.320597	−	0.126933i
$612$	3.39206	+	8.56736i	0.137116	+	0.346315i
$613$	−12.9215	+	10.6896i	−0.521894	+	0.431748i	−0.860703	−	0.509107i	$-0.829976\pi$
$613$	−12.9215	+	10.6896i	−0.521894	+	0.431748i	0.338809	+	0.940855i	$0.389976\pi$
$614$	13.3047	−	3.41607i	0.536935	−	0.137862i
$615$		0			0
$616$	68.4224	−	27.0904i	2.75682	−	1.09150i
$617$	−29.7693	−	31.7011i	−1.19847	−	1.27624i	−0.951653	−	0.307175i	$-0.900616\pi$
$617$	−29.7693	−	31.7011i	−1.19847	−	1.27624i	−0.246814	−	0.969063i	$-0.579384\pi$
$618$	2.03340	−	2.79874i	0.0817955	−	0.112582i
$619$	17.1197	+	36.3812i	0.688099	+	1.46228i	0.877100	+	0.480308i	$0.159475\pi$
$619$	17.1197	+	36.3812i	0.688099	+	1.46228i	−0.189001	+	0.981977i	$0.560525\pi$
$620$		0			0
$621$	−6.10887	+	3.35838i	−0.245140	+	0.134767i
$622$	−8.19834	+	1.56392i	−0.328723	+	0.0627073i
$623$	0.834444	+	3.24994i	0.0334313	+	0.130206i
$624$	−0.256058			−0.0102505
$625$		0			0
$626$	−13.7405			−0.549180
$627$	−1.21658	−	4.73825i	−0.0485854	−	0.189228i
$628$	−17.5863	+	3.35477i	−0.701771	+	0.133870i
$629$	1.18287	−	0.650291i	0.0471643	−	0.0259288i
$630$		0			0
$631$	−4.85565	−	10.3188i	−0.193300	−	0.410784i	0.784557	−	0.620057i	$-0.212890\pi$
$631$	−4.85565	−	10.3188i	−0.193300	−	0.410784i	−0.977857	+	0.209273i	$0.932890\pi$
$632$	21.5546	−	29.6674i	0.857396	−	1.18010i
$633$	2.28227	+	2.43037i	0.0907121	+	0.0965986i
$634$	24.1799	−	9.57350i	0.960306	−	0.380212i
$635$		0			0
$636$	2.28897	−	0.587708i	0.0907636	−	0.0233041i
$637$	−12.5054	+	10.3454i	−0.495482	+	0.409898i
$638$	5.34528	+	13.5006i	0.211622	+	0.534495i
$639$	17.4106	+	6.89335i	0.688753	+	0.272697i
$640$		0			0
$641$	−6.74084	+	10.6219i	−0.266247	+	0.419538i	−0.950978	−	0.309257i	$-0.899920\pi$
$641$	−6.74084	+	10.6219i	−0.266247	+	0.419538i	0.684731	+	0.728796i	$0.259920\pi$
$642$	0.450899	−	0.820183i	0.0177956	−	0.0323700i
$643$	−8.39431	−	11.5538i	−0.331039	−	0.455636i	0.610758	−	0.791817i	$-0.290865\pi$
$643$	−8.39431	−	11.5538i	−0.331039	−	0.455636i	−0.941797	+	0.336181i	$0.890865\pi$
$644$	−3.08942	+	16.1953i	−0.121740	+	0.638184i
$645$		0			0
$646$	−2.67631	+	5.68745i	−0.105298	+	0.223770i
$647$	9.81618	+	17.8556i	0.385914	+	0.701975i	0.995902	−	0.0904357i	$-0.0288260\pi$
$647$	9.81618	+	17.8556i	0.385914	+	0.701975i	−0.609989	+	0.792410i	$0.708826\pi$
$648$	−23.3754	−	1.47065i	−0.918271	−	0.0577727i
$649$	−17.0377	−	12.3786i	−0.668789	−	0.485903i
$650$		0			0
$651$	−10.1752	+	7.39270i	−0.398797	+	0.289743i
$652$	−4.21121	+	2.67252i	−0.164924	+	0.104664i
$653$	−3.70674	+	29.3419i	−0.145056	+	1.14824i	0.736595	+	0.676334i	$0.236433\pi$
$653$	−3.70674	+	29.3419i	−0.145056	+	1.14824i	−0.881651	+	0.471903i	$0.843567\pi$
$654$	−0.626412	−	0.0791343i	−0.0244947	−	0.00309440i
$655$		0			0
$656$	3.11697	+	1.71357i	0.121697	+	0.0669037i
$657$	−18.7028	−	6.07691i	−0.729666	−	0.237083i
$658$	−17.4882	+	8.22930i	−0.681759	+	0.320812i
$659$	−18.8416	−	4.83769i	−0.733963	−	0.188450i	−0.136833	−	0.990594i	$-0.543692\pi$
$659$	−18.8416	−	4.83769i	−0.733963	−	0.188450i	−0.597130	+	0.802144i	$0.703692\pi$
$660$		0			0
$661$	12.1626	−	14.7021i	0.473072	−	0.571846i	−0.478963	−	0.877835i	$-0.658987\pi$
$661$	12.1626	−	14.7021i	0.473072	−	0.571846i	0.952035	+	0.305989i	$0.0989872\pi$
$662$	6.54796	+	4.15546i	0.254494	+	0.161507i
$663$	1.56538	−	0.0984851i	0.0607942	−	0.00382484i
$664$	−28.1338	−	44.3317i	−1.09180	−	1.72040i
$665$		0			0
$666$	0.0810009	+	1.28747i	0.00313872	+	0.0498886i
$667$	−8.84813	−	1.68787i	−0.342601	−	0.0653546i
$668$	11.2583	−	3.65805i	0.435598	−	0.141534i
$669$	2.66598	−	2.50352i	0.103073	−	0.0967917i
$670$		0			0
$671$	8.78728	+	46.0645i	0.339229	+	1.77830i
$672$	5.00892	−	5.33396i	0.193223	−	0.205762i
$673$	3.94884	−	9.97363i	0.152217	−	0.384455i	−0.833580	−	0.552399i	$-0.813713\pi$
$673$	3.94884	−	9.97363i	0.152217	−	0.384455i	0.985797	+	0.167944i	$0.0537126\pi$
$674$	−7.19039	−	22.1297i	−0.276963	−	0.852406i
$675$		0			0
$676$	3.55750	−	10.9489i	0.136827	−	0.421110i
$677$	−26.7322	−	22.1148i	−1.02740	−	0.849940i	−0.0386108	−	0.999254i	$-0.512293\pi$
$677$	−26.7322	−	22.1148i	−1.02740	−	0.849940i	−0.988790	+	0.149315i	$0.952293\pi$
$678$	3.58101	+	1.68510i	0.137528	+	0.0647158i
$679$	−3.91683	−	3.67815i	−0.150314	−	0.141155i
$680$		0			0
$681$	3.31873	−	0.419253i	0.127174	−	0.0160658i
$682$			53.5280i			2.04969i
$683$	2.08208	+	16.4814i	0.0796686	+	0.630642i	0.980507	+	0.196487i	$0.0629532\pi$
$683$	2.08208	+	16.4814i	0.0796686	+	0.630642i	−0.900838	+	0.434156i	$0.857047\pi$
$684$	4.97996	+	6.01974i	0.190414	+	0.230171i
$685$		0			0
$686$	−0.637787	+	10.1373i	−0.0243508	+	0.387045i
$687$	−1.90565	+	7.42201i	−0.0727050	+	0.283167i
$688$	0.720467	−	2.80603i	0.0274676	−	0.106979i
$689$	−0.664873	+	10.5678i	−0.0253296	+	0.402603i
$690$		0			0
$691$	8.98969	+	10.8667i	0.341984	+	0.413388i	0.913264	−	0.407367i	$-0.133553\pi$
$691$	8.98969	+	10.8667i	0.341984	+	0.413388i	−0.571280	+	0.820755i	$0.693553\pi$
$692$	0.620466	+	4.91149i	0.0235866	+	0.186707i
$693$		−	72.8645i		−	2.76789i
$694$	−21.3554	+	2.69781i	−0.810639	+	0.102407i
$695$		0			0
$696$	1.77817	+	1.66982i	0.0674015	+	0.0632942i
$697$	−19.7143	−	9.27683i	−0.746731	−	0.351385i
$698$	−5.33635	−	4.41461i	−0.201984	−	0.167095i
$699$	−1.68655	+	5.19068i	−0.0637913	+	0.196330i
$700$		0			0
$701$	−10.3474	−	31.8460i	−0.390816	−	1.20281i	−0.932173	−	0.362014i	$-0.882089\pi$
$701$	−10.3474	−	31.8460i	−0.390816	−	1.20281i	0.541357	−	0.840793i	$-0.317911\pi$
$702$	−1.12457	+	2.84034i	−0.0424442	+	0.107202i
$703$	0.783458	−	0.834298i	0.0295487	−	0.0314661i
$704$	−6.90061	−	36.1743i	−0.260076	−	1.36337i
$705$		0			0
$706$	−5.47526	+	5.14161i	−0.206064	+	0.193507i
$707$	33.9211	−	11.0216i	1.27573	−	0.414511i
$708$	−1.25509	−	0.239421i	−0.0471692	−	0.00899801i
$709$	1.45572	+	23.1380i	0.0546707	+	0.868966i	0.925824	+	0.377955i	$0.123373\pi$
$709$	1.45572	+	23.1380i	0.0546707	+	0.868966i	−0.871153	+	0.491011i	$0.836627\pi$
$710$		0			0
$711$	−19.4555	−	30.6569i	−0.729637	−	1.14972i
$712$	2.39424	−	0.150633i	0.0897278	−	0.00564520i
$713$	−28.0368	−	17.7927i	−1.04999	−	0.666343i
$714$	2.26716	−	2.74052i	0.0848463	−	0.102562i
$715$		0			0
$716$	6.66187	+	1.71048i	0.248966	+	0.0639235i
$717$	3.80301	−	1.78956i	0.142026	−	0.0668324i
$718$	20.3743	+	6.62002i	0.760363	+	0.247057i
$719$	16.7905	+	9.23066i	0.626180	+	0.344245i	0.763046	−	0.646344i	$-0.223703\pi$
$719$	16.7905	+	9.23066i	0.626180	+	0.344245i	−0.136866	+	0.990590i	$0.543703\pi$
$720$		0			0
$721$	−45.3542	−	5.72957i	−1.68908	−	0.213380i
$722$	1.55237	−	12.2883i	0.0577734	−	0.457323i
$723$	−3.90380	+	2.47742i	−0.145184	+	0.0921364i
$724$	1.62995	−	1.18423i	0.0605766	−	0.0440115i
$725$		0			0
$726$	6.78152	+	4.92706i	0.251686	+	0.182860i
$727$	−6.50973	−	0.409557i	−0.241432	−	0.0151896i	−0.0583867	−	0.998294i	$-0.518596\pi$
$727$	−6.50973	−	0.409557i	−0.241432	−	0.0151896i	−0.183046	+	0.983104i	$0.558596\pi$
$728$	9.63761	+	17.5307i	0.357194	+	0.649733i
$729$	−9.04798	+	19.2279i	−0.335111	+	0.712146i
$730$		0			0
$731$	−3.32522	+	17.4314i	−0.122988	+	0.644724i
$732$	1.67236	+	2.30181i	0.0618122	+	0.0850773i
$733$	−9.81270	+	17.8492i	−0.362440	+	0.659276i	−0.993164	−	0.116732i	$-0.962758\pi$
$733$	−9.81270	+	17.8492i	−0.362440	+	0.659276i	0.630723	+	0.776008i	$0.282758\pi$
$734$	−8.28520	+	13.0554i	−0.305812	+	0.481883i
$735$		0			0
$736$	17.9619	+	7.11163i	0.662086	+	0.262138i
$737$	10.7348	+	27.1131i	0.395423	+	0.998723i
$738$	16.0438	−	13.2726i	0.590582	−	0.488572i
$739$	33.4390	−	8.58567i	1.23007	−	0.315829i	0.422917	−	0.906168i	$-0.361006\pi$
$739$	33.4390	−	8.58567i	1.23007	−	0.315829i	0.807155	+	0.590339i	$0.201006\pi$
$740$		0			0
$741$	1.23647	−	0.489554i	0.0454230	−	0.0179842i
$742$	16.4371	+	17.5037i	0.603424	+	0.642582i
$743$	−12.7494	+	17.5480i	−0.467729	+	0.643774i	−0.976089	−	0.217371i	$-0.930252\pi$
$743$	−12.7494	+	17.5480i	−0.467729	+	0.643774i	0.508360	+	0.861145i	$0.330252\pi$
$744$	3.82873	+	8.13647i	0.140368	+	0.298298i
$745$		0			0
$746$	13.0807	−	7.19116i	0.478917	−	0.263287i
$747$	−51.0668	+	9.74150i	−1.86843	+	0.356423i
$748$	4.89599	+	19.0686i	0.179015	+	0.697218i
$749$	−12.3682			−0.451923
$750$		0			0
$751$	−21.6995			−0.791826			−0.395913	−	0.918288i	$-0.629572\pi$
$751$	−21.6995			−0.791826			−0.395913	+	0.918288i	$0.629572\pi$
$752$	0.581256	+	2.26384i	0.0211962	+	0.0825538i
$753$	−2.07906	+	0.396602i	−0.0757652	+	0.0144530i
$754$	−3.45904	+	1.90163i	−0.125971	+	0.0692531i
$755$		0			0
$756$	−3.83606	−	8.15205i	−0.139516	−	0.296487i
$757$	18.5103	−	25.4773i	0.672769	−	0.925988i	−0.327050	−	0.945007i	$-0.606054\pi$
$757$	18.5103	−	25.4773i	0.672769	−	0.925988i	0.999819	+	0.0190196i	$0.00605449\pi$
$758$	23.3432	+	24.8580i	0.847863	+	0.902883i
$759$	−6.79509	+	2.69036i	−0.246646	+	0.0976541i
$760$		0			0
$761$	−14.1041	+	3.62131i	−0.511272	+	0.131272i	−0.495508	−	0.868603i	$-0.665018\pi$
$761$	−14.1041	+	3.62131i	−0.511272	+	0.131272i	−0.0157640	+	0.999876i	$0.505018\pi$
$762$	1.10787	−	0.916507i	0.0401338	−	0.0332015i
$763$	3.07145	+	7.75761i	0.111194	+	0.280844i
$764$	12.9992	+	5.14673i	0.470293	+	0.186202i
$765$		0			0
$766$	−4.94594	+	7.79356i	−0.178704	+	0.281593i
$767$	2.75806	−	5.01688i	0.0995876	−	0.181149i
$768$	−3.27775	−	4.51144i	−0.118276	−	0.162792i
$769$	−1.26960	+	6.65550i	−0.0457831	+	0.240003i	−0.997821	−	0.0659761i	$-0.978984\pi$
$769$	−1.26960	+	6.65550i	−0.0457831	+	0.240003i	0.952038	+	0.305979i	$0.0989839\pi$
$770$		0			0
$771$	1.83867	−	3.90738i	0.0662182	−	0.140721i
$772$	11.5656	+	21.0378i	0.416255	+	0.757165i
$773$	43.7526	+	2.75268i	1.57367	+	0.0990070i	0.825463	−	0.564456i	$-0.190914\pi$
$773$	43.7526	+	2.75268i	1.57367	+	0.0990070i	0.748209	+	0.663463i	$0.230914\pi$
$774$	−13.7203	−	9.96842i	−0.493168	−	0.358307i
$775$		0			0
$776$	−3.10792	+	2.25804i	−0.111568	+	0.0810588i
$777$	−0.546795	+	0.347007i	−0.0196162	+	0.0124488i
$778$	−0.0856308	+	0.677837i	−0.00307001	+	0.0243017i
$779$	−18.3276	−	2.31532i	−0.656656	−	0.0829549i
$780$		0			0
$781$	35.0595	+	19.2741i	1.25453	+	0.689682i
$782$	8.93086	+	2.90181i	0.319367	+	0.103769i
$783$	4.45379	−	2.09579i	0.159165	−	0.0748975i
$784$	4.31085	+	1.10684i	0.153959	+	0.0395299i
$785$		0			0
$786$	−2.50741	+	3.03094i	−0.0894365	+	0.108110i
$787$	24.3047	+	15.4242i	0.866369	+	0.549814i	0.893115	−	0.449828i	$-0.148515\pi$
$787$	24.3047	+	15.4242i	0.866369	+	0.549814i	−0.0267465	+	0.999642i	$0.508515\pi$
$788$	13.3618	−	0.840653i	0.475994	−	0.0299470i
$789$	−0.280613	−	0.442176i	−0.00999010	−	0.0157419i
$790$		0			0
$791$	−3.28387	−	52.1955i	−0.116761	−	1.85586i
$792$	−51.1730	−	9.76177i	−1.81835	−	0.346869i
$793$	−12.1244	+	3.93944i	−0.430549	+	0.139894i
$794$	−14.7544	+	13.8553i	−0.523615	+	0.491707i
$795$		0			0
$796$	1.00571	+	5.27214i	0.0356466	+	0.186866i
$797$	8.47048	−	9.02014i	0.300040	−	0.319510i	−0.561228	−	0.827661i	$-0.689671\pi$
$797$	8.47048	−	9.02014i	0.300040	−	0.319510i	0.861268	+	0.508151i	$0.169671\pi$
$798$	1.11014	−	2.80389i	0.0392985	−	0.0992568i
$799$	−4.42415	−	13.6161i	−0.156515	−	0.481704i
$800$		0			0
$801$	0.734012	−	2.25906i	0.0259351	−	0.0798199i
$802$	−22.8149	−	18.8741i	−0.805621	−	0.666467i
$803$	−38.0172	−	17.8895i	−1.34160	−	0.631308i
$804$	1.28971	+	1.21112i	0.0454846	+	0.0427129i
$805$		0			0
$806$	−14.4367	+	1.82378i	−0.508510	+	0.0642398i
$807$		−	0.0834343i		−	0.00293702i
$808$	−3.19607	−	25.2995i	−0.112437	−	0.890032i
$809$	−22.0951	−	26.7084i	−0.776822	−	0.939016i	0.222533	−	0.974925i	$-0.428567\pi$
$809$	−22.0951	−	26.7084i	−0.776822	−	0.939016i	−0.999355	+	0.0359088i	$0.988567\pi$
$810$		0			0
$811$	−1.74281	+	27.7011i	−0.0611982	+	0.972718i	0.840901	+	0.541189i	$0.182026\pi$
$811$	−1.74281	+	27.7011i	−0.0611982	+	0.972718i	−0.902099	+	0.431529i	$0.857974\pi$
$812$	2.89513	−	11.2758i	0.101599	−	0.395702i
$813$	0.868326	−	3.38191i	0.0304535	−	0.118609i
$814$	−0.173063	+	2.75076i	−0.00606585	+	0.0964139i
$815$		0			0
$816$	−0.274166	−	0.331409i	−0.00959772	−	0.0116016i
$817$	1.88577	+	14.9274i	0.0659749	+	0.522245i
$818$		−	18.7359i		−	0.655086i
$819$	19.6518	−	2.48260i	0.686690	−	0.0867491i
$820$		0			0
$821$	5.04523	+	4.73778i	0.176080	+	0.165350i	0.767576	−	0.640958i	$-0.221463\pi$
$821$	5.04523	+	4.73778i	0.176080	+	0.165350i	−0.591497	+	0.806308i	$0.701463\pi$
$822$	3.68751	+	1.73521i	0.128617	+	0.0605224i
$823$	17.9832	+	14.8770i	0.626856	+	0.518581i	0.895732	−	0.444594i	$-0.146652\pi$
$823$	17.9832	+	14.8770i	0.626856	+	0.518581i	−0.268876	+	0.963175i	$0.586652\pi$
$824$	−10.1001	+	31.0848i	−0.351852	+	1.08289i
$825$		0			0
$826$	−4.01178	−	12.3470i	−0.139588	−	0.429607i
$827$	−12.2872	+	31.0339i	−0.427267	+	1.07915i	0.543559	+	0.839371i	$0.317076\pi$
$827$	−12.2872	+	31.0339i	−0.427267	+	1.07915i	−0.970826	+	0.239783i	$0.922924\pi$
$828$	7.98980	−	8.50828i	0.277665	−	0.295683i
$829$	9.18343	+	48.1412i	0.318954	+	1.67201i	0.675210	+	0.737626i	$0.264053\pi$
$829$	9.18343	+	48.1412i	0.318954	+	1.67201i	−0.356256	+	0.934388i	$0.615947\pi$
$830$		0			0
$831$	−1.22295	+	1.14843i	−0.0424237	+	0.0398385i
$832$	9.52120	−	3.09363i	0.330088	−	0.107252i
$833$	−26.7795	−	5.10846i	−0.927854	−	0.176998i
$834$	−0.0104850	−	0.166655i	−0.000363067	−	0.00577079i
$835$		0			0
$836$	8.94409	+	14.0936i	0.309338	+	0.487438i
$837$	18.1097	−	1.13937i	0.625962	−	0.0393822i
$838$	−6.53782	−	4.14903i	−0.225845	−	0.143326i
$839$	12.0487	−	14.5644i	0.415969	−	0.502820i	−0.520359	−	0.853948i	$-0.674202\pi$
$839$	12.0487	−	14.5644i	0.415969	−	0.502820i	0.936328	+	0.351128i	$0.114202\pi$
$840$		0			0
$841$	−21.9285	−	5.63028i	−0.756156	−	0.194148i
$842$	−18.0432	+	8.49047i	−0.621809	+	0.292601i
$843$	8.89500	+	2.89016i	0.306360	+	0.0995424i
$844$	−9.96897	−	5.48049i	−0.343146	−	0.188646i
$845$		0			0
$846$	13.5745	+	1.71485i	0.466699	+	0.0589579i
$847$	13.8831	−	109.896i	0.477029	−	3.77607i
$848$	2.45168	−	1.55588i	0.0841910	−	0.0534292i
$849$	8.84244	−	6.42441i	0.303472	−	0.220485i
$850$		0			0
$851$	−1.38326	−	1.00500i	−0.0474176	−	0.0344509i
$852$	2.42256	+	0.152415i	0.0829956	+	0.00522164i
$853$	−0.299653	−	0.545066i	−0.0102599	−	0.0186627i	0.871127	−	0.491058i	$-0.163390\pi$
$853$	−0.299653	−	0.545066i	−0.0102599	−	0.0186627i	−0.881387	+	0.472395i	$0.843390\pi$
$854$	−12.3088	+	26.1574i	−0.421197	+	0.895089i
$855$		0			0
$856$	−1.65698	+	8.68620i	−0.0566344	+	0.296888i
$857$	13.8679	+	19.0875i	0.473718	+	0.652017i	0.977282	−	0.211941i	$-0.0679784\pi$
$857$	13.8679	+	19.0875i	0.473718	+	0.652017i	−0.503565	+	0.863958i	$0.667978\pi$
$858$	−1.54287	+	2.80647i	−0.0526726	+	0.0958112i
$859$	21.8559	−	34.4395i	0.745715	−	1.17506i	−0.233524	−	0.972351i	$-0.575026\pi$
$859$	21.8559	−	34.4395i	0.745715	−	1.17506i	0.979239	−	0.202708i	$-0.0649743\pi$
$860$		0			0
$861$	9.71907	+	3.84805i	0.331225	+	0.131141i
$862$	−1.55834	−	3.93591i	−0.0530772	−	0.134058i
$863$	35.0102	−	28.9630i	1.19176	−	0.985912i	0.191772	−	0.981439i	$-0.438576\pi$
$863$	35.0102	−	28.9630i	1.19176	−	0.985912i	0.999990	−	0.00447214i	$-0.00142353\pi$
$864$	−10.2250	+	2.62533i	−0.347861	+	0.0893155i
$865$		0			0
$866$	−18.2264	+	7.21635i	−0.619359	+	0.245221i
$867$	−2.05257	−	2.18577i	−0.0697090	−	0.0742326i
$868$	25.2251	−	34.7194i	0.856197	−	1.17845i
$869$	−33.0306	−	70.1935i	−1.12048	−	2.38115i
$870$		0			0
$871$	−6.94674	+	3.81900i	−0.235381	+	0.129402i
$872$	5.85968	−	1.11779i	0.198434	−	0.0378533i
$873$	0.945947	+	3.68422i	0.0320155	+	0.124692i
$874$	7.96189			0.269315
$875$		0			0
$876$	−2.54916			−0.0861282
$877$	−14.0544	−	54.7385i	−0.474585	−	1.84839i	−0.527155	−	0.849769i	$-0.676741\pi$
$877$	−14.0544	−	54.7385i	−0.474585	−	1.84839i	0.0525704	−	0.998617i	$-0.483259\pi$
$878$	−29.3412	+	5.59713i	−0.990217	+	0.188894i
$879$	1.71892	−	0.944984i	0.0579777	−	0.0318735i
$880$		0			0
$881$	−6.45240	−	13.7120i	−0.217387	−	0.461970i	0.766154	−	0.642657i	$-0.222168\pi$
$881$	−6.45240	−	13.7120i	−0.217387	−	0.461970i	−0.983541	+	0.180687i	$0.942168\pi$
$882$	15.3142	−	21.0782i	0.515657	−	0.709742i
$883$	−30.0857	−	32.0380i	−1.01246	−	1.07817i	−0.996931	−	0.0782859i	$-0.975055\pi$
$883$	−30.0857	−	32.0380i	−1.01246	−	1.07817i	−0.0155336	−	0.999879i	$-0.504945\pi$
$884$	−4.97606	+	1.97016i	−0.167363	+	0.0662637i
$885$		0			0
$886$	−7.52842	+	1.93297i	−0.252922	+	0.0649394i
$887$	21.7371	−	17.9825i	0.729859	−	0.603792i	−0.196469	−	0.980510i	$-0.562947\pi$
$887$	21.7371	−	17.9825i	0.729859	−	0.603792i	0.926328	+	0.376718i	$0.122947\pi$
$888$	0.170449	+	0.430505i	0.00571989	+	0.0144468i
$889$	−17.6659	−	6.99444i	−0.592496	−	0.234586i
$890$		0			0
$891$	−26.5491	+	41.8348i	−0.889430	+	1.40152i
$892$	−6.01178	+	10.9354i	−0.201289	+	0.366144i
$893$	−7.13502	−	9.82052i	−0.238764	−	0.328631i
$894$	−0.159179	+	0.834448i	−0.00532376	+	0.0279081i
$895$		0			0
$896$	−9.13833	+	19.4199i	−0.305290	+	0.648775i
$897$	−0.957119	−	1.74099i	−0.0319573	−	0.0581301i
$898$	−21.1296	−	1.32936i	−0.705104	−	0.0443614i
$899$	18.9686	+	13.7815i	0.632637	+	0.459638i
$900$		0			0
$901$	−14.3896	+	10.4546i	−0.479386	+	0.348295i
$902$	37.5624	−	23.8378i	1.25069	−	0.793713i
$903$	1.06707	−	8.44670i	0.0355097	−	0.281089i
$904$	−37.0970	−	4.68645i	−1.23383	−	0.155869i
$905$		0			0
$906$	1.47331	+	0.809961i	0.0489475	+	0.0269091i
$907$	−33.5504	−	10.9012i	−1.11402	−	0.361967i	−0.306538	−	0.951858i	$-0.599171\pi$
$907$	−33.5504	−	10.9012i	−1.11402	−	0.361967i	−0.807483	+	0.589891i	$0.799171\pi$
$908$	−10.3278	+	4.85988i	−0.342739	+	0.161281i
$909$	−24.4558	−	6.27919i	−0.811149	−	0.208268i
$910$		0			0
$911$	13.5488	−	16.3777i	0.448892	−	0.542617i	−0.496721	−	0.867910i	$-0.665463\pi$
$911$	13.5488	−	16.3777i	0.448892	−	0.542617i	0.945613	+	0.325293i	$0.105463\pi$
$912$	−0.307911	−	0.195406i	−0.0101959	−	0.00647055i
$913$	−110.855	+	6.97441i	−3.66877	+	0.230819i
$914$	−0.362531	−	0.571258i	−0.0119915	−	0.0188955i
$915$		0			0
$916$	−1.64176	−	26.0950i	−0.0542452	−	0.862203i
$917$	51.0607	+	9.74035i	1.68617	+	0.321655i
$918$	−4.88027	+	1.58570i	−0.161073	+	0.0523358i
$919$	−10.3109	+	9.68262i	−0.340127	+	0.319400i	−0.835721	−	0.549154i	$-0.814950\pi$
$919$	−10.3109	+	9.68262i	−0.340127	+	0.319400i	0.495595	+	0.868554i	$0.334950\pi$
$920$		0			0
$921$	−0.914735	−	4.79521i	−0.0301415	−	0.158008i
$922$	−5.91530	+	6.29915i	−0.194810	+	0.207451i
$923$	−4.00377	+	10.1124i	−0.131786	+	0.332852i
$924$	−2.91874	−	8.98296i	−0.0960195	−	0.295518i
$925$		0			0
$926$	−7.57730	+	23.3205i	−0.249005	+	0.766360i
$927$	24.9355	+	20.6284i	0.818989	+	0.677526i
$928$	−12.3424	−	5.80789i	−0.405159	−	0.190653i
$929$	20.7835	+	19.5170i	0.681885	+	0.640332i	0.946003	−	0.324158i	$-0.105081\pi$
$929$	20.7835	+	19.5170i	0.681885	+	0.640332i	−0.264118	+	0.964490i	$0.585081\pi$
$930$		0			0
$931$	−22.9327	+	2.89707i	−0.751588	+	0.0949477i
$932$		−	18.6229i		−	0.610015i
$933$	0.371752	+	2.94272i	0.0121706	+	0.0963403i
$934$	8.11889	+	9.81405i	0.265658	+	0.321126i
$935$		0			0
$936$	0.889243	−	14.1341i	0.0290658	−	0.461988i
$937$	−3.88410	+	15.1276i	−0.126888	+	0.494196i	0.873090	+	0.487559i	$0.162113\pi$
$937$	−3.88410	+	15.1276i	−0.126888	+	0.494196i	−0.999978	+	0.00663687i	$0.997887\pi$
$938$	−4.47054	+	17.4116i	−0.145968	+	0.568509i
$939$	−0.306617	+	4.87353i	−0.0100061	+	0.159042i
$940$		0			0
$941$	23.0918	+	27.9132i	0.752771	+	0.909943i	0.998230	−	0.0594634i	$-0.0189390\pi$
$941$	23.0918	+	27.9132i	0.752771	+	0.909943i	−0.245460	+	0.969407i	$0.578939\pi$
$942$	−0.613155	−	4.85362i	−0.0199777	−	0.158140i
$943$			27.5981i			0.898718i
$944$	−1.55757	+	0.196767i	−0.0506946	+	0.00640422i
$945$		0			0
$946$	−26.4138	−	24.8042i	−0.858785	−	0.806453i
$947$	20.1857	+	9.49865i	0.655946	+	0.308665i	0.724797	−	0.688962i	$-0.241933\pi$
$947$	20.1857	+	9.49865i	0.655946	+	0.308665i	−0.0688516	+	0.997627i	$0.521933\pi$
$948$	−3.62656	−	3.00015i	−0.117785	−	0.0974403i
$949$	3.52956	−	10.8629i	0.114575	−	0.352624i
$950$		0			0
$951$	−2.85600	−	8.78986i	−0.0926121	−	0.285031i
$952$	−12.3704	+	31.2442i	−0.400928	+	1.01263i
$953$	−20.3042	+	21.6218i	−0.657718	+	0.700399i	−0.968199	−	0.250181i	$-0.919510\pi$
$953$	−20.3042	+	21.6218i	−0.657718	+	0.700399i	0.310481	+	0.950580i	$0.399510\pi$
$954$	−3.18515	−	16.6971i	−0.103123	−	0.540590i
$955$		0			0
$956$	−10.4544	+	9.81737i	−0.338121	+	0.317517i
$957$	4.90774	−	1.59462i	0.158645	−	0.0515468i
$958$	8.07560	+	1.54050i	0.260911	+	0.0497714i
$959$	−3.38152	−	53.7477i	−0.109195	−	1.73560i
$960$		0			0
$961$	29.7028	+	46.8041i	0.958154	+	1.50981i
$962$	−0.747784	+	0.0470466i	−0.0241095	+	0.00151684i
$963$	7.39262	+	4.69150i	0.238224	+	0.151182i
$964$	10.0562	−	12.1559i	0.323889	−	0.391515i
$965$		0			0
$966$	−4.36370	−	1.12041i	−0.140400	−	0.0360485i
$967$	9.00738	−	4.23855i	0.289658	−	0.136303i	−0.275461	−	0.961312i	$-0.588830\pi$
$967$	9.00738	−	4.23855i	0.289658	−	0.136303i	0.565119	+	0.825010i	$0.308830\pi$
$968$	−75.3204	−	24.4731i	−2.42089	−	0.786594i
$969$	1.95753	+	1.07616i	0.0628849	+	0.0345713i
$970$		0			0
$971$	42.8776	+	5.41671i	1.37601	+	0.173830i	0.778305	−	0.627886i	$-0.216080\pi$
$971$	42.8776	+	5.41671i	1.37601	+	0.173830i	0.597704	+	0.801717i	$0.296080\pi$
$972$	−1.20651	+	9.55052i	−0.0386989	+	0.306333i
$973$	−1.86311	+	1.18236i	−0.0597285	+	0.0379048i
$974$	29.1113	−	21.1506i	0.932785	−	0.677708i
$975$		0			0
$976$	2.82825	+	2.05485i	0.0905302	+	0.0657740i
$977$	23.5819	+	1.48365i	0.754451	+	0.0474660i	0.435358	−	0.900257i	$-0.356622\pi$
$977$	23.5819	+	1.48365i	0.754451	+	0.0474660i	0.319093	+	0.947723i	$0.396622\pi$
$978$	−0.656582	−	1.19432i	−0.0209952	−	0.0381901i
$979$	2.16082	−	4.59199i	0.0690603	−	0.146761i
$980$		0			0
$981$	1.10677	−	5.80190i	0.0353365	−	0.185240i
$982$	−11.0974	−	15.2743i	−0.354133	−	0.487422i
$983$	18.3165	−	33.3175i	0.584205	−	1.06266i	−0.404748	−	0.914428i	$-0.632641\pi$
$983$	18.3165	−	33.3175i	0.584205	−	1.06266i	0.988952	−	0.148236i	$-0.0473594\pi$
$984$	4.00458	−	6.31020i	0.127661	−	0.201162i
$985$		0			0
$986$	−6.16488	−	2.44085i	−0.196330	−	0.0777325i
$987$	2.52856	+	6.38641i	0.0804849	+	0.203282i
$988$	−3.49636	+	2.89244i	−0.111234	+	0.0920208i
$989$	21.7719	−	5.59006i	0.692305	−	0.177754i
$990$		0			0
$991$	6.67915	−	2.64446i	0.212170	−	0.0840041i	−0.259635	−	0.965707i	$-0.583602\pi$
$991$	6.67915	−	2.64446i	0.212170	−	0.0840041i	0.471806	+	0.881703i	$0.343602\pi$
$992$	−34.4225	−	36.6562i	−1.09291	−	1.16384i
$993$	1.61999	−	2.22973i	0.0514090	−	0.0707584i
$994$	10.5011	+	22.3160i	0.333075	+	0.707821i
$995$		0			0
$996$	−5.90545	+	3.24655i	−0.187121	+	0.102871i
$997$	41.0229	−	7.82553i	1.29921	−	0.247837i	0.509048	−	0.860738i	$-0.329998\pi$
$997$	41.0229	−	7.82553i	1.29921	−	0.247837i	0.790160	+	0.612901i	$0.209998\pi$
$998$	7.26130	+	28.2809i	0.229853	+	0.895216i
$999$	0.934325			0.0295607

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.h.b.274.8		440
5.2	odd	4		625.2.g.a.351.7		220
5.3	odd	4		125.2.g.a.21.5	yes	220
5.4	even	2	inner	625.2.h.b.274.15		440
125.6	even	25	inner	625.2.h.b.349.15		440
125.33	odd	100		125.2.g.a.6.5	✓	220
125.92	odd	100		625.2.g.a.276.7		220
125.119	even	50	inner	625.2.h.b.349.8		440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.g.a.6.5	✓	220	125.33	odd	100
125.2.g.a.21.5	yes	220	5.3	odd	4
625.2.g.a.276.7		220	125.92	odd	100
625.2.g.a.351.7		220	5.2	odd	4
625.2.h.b.274.8		440	1.1	even	1	trivial
625.2.h.b.274.15		440	5.4	even	2	inner
625.2.h.b.349.8		440	125.119	even	50	inner
625.2.h.b.349.15		440	125.6	even	25	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.h (of order \(50\), degree \(20\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.231876 - 0.903097i) q^{2} +(-0.325489 + 0.0620903i) q^{3} +(0.990795 - 0.544694i) q^{4} +(0.131547 + 0.279551i) q^{6} +(2.39974 - 3.30296i) q^{7} +(-1.99818 - 2.12785i) q^{8} +(-2.68724 + 1.06395i) q^{9} +O(q^{10})\)	\(q+(-0.231876 - 0.903097i) q^{2} +(-0.325489 + 0.0620903i) q^{3} +(0.990795 - 0.544694i) q^{4} +(0.131547 + 0.279551i) q^{6} +(2.39974 - 3.30296i) q^{7} +(-1.99818 - 2.12785i) q^{8} +(-2.68724 + 1.06395i) q^{9} +(-5.98107 + 1.53568i) q^{11} +(-0.288672 + 0.238811i) q^{12} +(-0.617961 - 1.56079i) q^{13} +(-3.53934 - 1.40132i) q^{14} +(-0.246660 + 0.388674i) q^{16} +(1.35843 - 2.47098i) q^{17} +(1.58396 + 2.18014i) q^{18} +(0.447990 - 2.34845i) q^{19} +(-0.576007 + 1.22408i) q^{21} +(2.77373 + 5.04540i) q^{22} +(-3.56467 - 0.224270i) q^{23} +(0.782505 + 0.568523i) q^{24} +(-1.26626 + 0.919989i) q^{26} +(1.64793 - 1.04581i) q^{27} +(0.578549 - 4.57968i) q^{28} +(2.50206 + 0.316084i) q^{29} +(8.14699 + 4.47885i) q^{31} +(-5.14404 - 1.67140i) q^{32} +(1.85142 - 0.871213i) q^{33} +(-2.54652 - 0.653835i) q^{34} +(-2.08298 + 2.51789i) q^{36} +(0.404186 + 0.256504i) q^{37} +(-2.22475 + 0.139970i) q^{38} +(0.298050 + 0.469651i) q^{39} +(-0.485173 - 7.71160i) q^{41} +(1.23902 + 0.236356i) q^{42} +(-5.98533 + 1.94475i) q^{43} +(-5.08954 + 4.77940i) q^{44} +(0.624023 + 3.27124i) q^{46} +(3.47567 - 3.70121i) q^{47} +(0.0561522 - 0.141824i) q^{48} +(-2.98768 - 9.19512i) q^{49} +(-0.288730 + 0.888621i) q^{51} +(-1.46243 - 1.20983i) q^{52} +(-5.70747 - 2.68573i) q^{53} +(-1.32658 - 1.24574i) q^{54} +(-11.8233 + 1.49363i) q^{56} +0.792208i q^{57} +(-0.294713 - 2.33290i) q^{58} +(2.17390 + 2.62780i) q^{59} +(0.476848 - 7.57928i) q^{61} +(2.15574 - 8.39606i) q^{62} +(-2.93449 + 11.4291i) q^{63} +(-0.374467 + 5.95198i) q^{64} +(-1.21609 - 1.47000i) q^{66} +(-0.591868 - 4.68512i) q^{67} -3.18816i q^{68} +(1.17418 - 0.148334i) q^{69} +(-4.72298 - 4.43517i) q^{71} +(7.63354 + 3.59207i) q^{72} +(5.24267 + 4.33711i) q^{73} +(0.137927 - 0.424497i) q^{74} +(-0.835318 - 2.57085i) q^{76} +(-9.28074 + 23.4405i) q^{77} +(0.355030 - 0.378068i) q^{78} +(2.35405 + 12.3404i) q^{79} +(5.84915 - 5.49272i) q^{81} +(-6.85183 + 2.22629i) q^{82} +(17.6689 + 3.37053i) q^{83} +(0.0960429 + 1.52656i) q^{84} +(3.14415 + 4.95439i) q^{86} +(-0.834019 + 0.0524720i) q^{87} +(15.2190 + 9.65825i) q^{88} +(-0.523867 + 0.633247i) q^{89} +(-6.63818 - 1.70440i) q^{91} +(-3.65401 + 1.71945i) q^{92} +(-2.92985 - 0.951965i) q^{93} +(-4.14848 - 2.28064i) q^{94} +(1.77810 + 0.224627i) q^{96} +(0.164948 - 1.30570i) q^{97} +(-7.61132 + 4.83029i) q^{98} +(14.4387 - 10.4903i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q + 40 q^{4} - 40 q^{6} + 40 q^{9}+O(q^{10}) \) 440 * q + 40 * q^4 - 40 * q^6 + 40 * q^9	\( 440 q + 40 q^{4} - 40 q^{6} + 40 q^{9} - 30 q^{11} + 20 q^{14} + 20 q^{19} - 10 q^{21} - 30 q^{24} + 30 q^{26} + 20 q^{29} - 20 q^{31} - 10 q^{34} - 420 q^{36} - 10 q^{41} - 30 q^{44} + 40 q^{49} + 50 q^{51} - 120 q^{54} - 210 q^{56} - 10 q^{59} - 90 q^{64} + 110 q^{66} - 80 q^{69} - 170 q^{71} - 70 q^{74} + 70 q^{76} + 110 q^{81} - 230 q^{84} + 80 q^{86} - 110 q^{89} - 210 q^{91} - 120 q^{94} + 270 q^{96} - 90 q^{99}+O(q^{100}) \) 440 * q + 40 * q^4 - 40 * q^6 + 40 * q^9 - 30 * q^11 + 20 * q^14 + 20 * q^19 - 10 * q^21 - 30 * q^24 + 30 * q^26 + 20 * q^29 - 20 * q^31 - 10 * q^34 - 420 * q^36 - 10 * q^41 - 30 * q^44 + 40 * q^49 + 50 * q^51 - 120 * q^54 - 210 * q^56 - 10 * q^59 - 90 * q^64 + 110 * q^66 - 80 * q^69 - 170 * q^71 - 70 * q^74 + 70 * q^76 + 110 * q^81 - 230 * q^84 + 80 * q^86 - 110 * q^89 - 210 * q^91 - 120 * q^94 + 270 * q^96 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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